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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%D8%B1%D8%AA%D9%86_%D9%82%D9%88%D8%AA%D8%B3%D9%88%DB%8C%D9%84%D8%B1" title="مارتن قوتسویلر – South Azerbaijani" lang="azb" hreflang="azb" data-title="مارتن قوتسویلر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Martin_Gutzwiller" title="Martin Gutzwiller – Catalan" lang="ca" hreflang="ca" data-title="Martin Gutzwiller" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Martin_Gutzwiller" title="Martin Gutzwiller – German" lang="de" hreflang="de" 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Swiss-American physicist (1925–2014)</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Martin C. Gutzwiller</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:MGutzwiller.jpg" class="mw-file-description"><img alt="Martin Gutzwiller" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/MGutzwiller.jpg/220px-MGutzwiller.jpg" decoding="async" width="220" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/MGutzwiller.jpg/330px-MGutzwiller.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/MGutzwiller.jpg/440px-MGutzwiller.jpg 2x" data-file-width="538" data-file-height="532" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1925-10-12</span>)</span>October 12, 1925<sup id="cite_ref-acp_1-0" class="reference"><a href="#cite_note-acp-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /><div style="display:inline" class="birthplace"><a href="/wiki/Basel" title="Basel">Basel</a>, <a href="/wiki/Switzerland" title="Switzerland">Switzerland</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">March 3, 2014<span style="display:none">(2014-03-03)</span> (aged 88)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Rio_Rancho" class="mw-redirect" title="Rio Rancho">Rio Rancho</a>, <a href="/wiki/New_Mexico" title="New Mexico">New Mexico</a></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a>,<sup id="cite_ref-acp_1-1" class="reference"><a href="#cite_note-acp-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /><a href="/wiki/University_of_Kansas" title="University of Kansas">University of Kansas</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data">Gutzwiller approximation <br /> Gutzwiller trace formula <br /> <a href="/wiki/Hadamard%E2%80%93Gutzwiller_model" class="mw-redirect" title="Hadamard–Gutzwiller model">Hadamard–Gutzwiller model</a><br /><a href="/wiki/Hubbard_model" title="Hubbard model">Hubbard model</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize for Mathematical Physics</a> <span style="font-size:85%;">(1993)</span><br /> <a href="/wiki/Max_Planck_Medal" title="Max Planck Medal">Max Planck Medal</a> <span style="font-size:85%;">(2003)</span></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a>, <a href="/wiki/Complex_Systems" class="mw-redirect" title="Complex Systems">Complex Systems</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/IBM" title="IBM">IBM</a>, <a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a>, <a href="/wiki/Yale_University" title="Yale University">Yale University</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Max_Dresden" title="Max Dresden">Max Dresden</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Martin Charles Gutzwiller</b> (12 October 1925 – 3 March 2014<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>) was a Swiss-American <a href="/wiki/Physicist" title="Physicist">physicist</a>, known for his work on <a href="/wiki/Field_theory_(physics)" class="mw-redirect" title="Field theory (physics)">field theory</a>, <a href="/wiki/Quantum_chaos" title="Quantum chaos">quantum chaos</a>, and <a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">complex systems</a>. He spent most of his career at <a href="/wiki/IBM_Research" title="IBM Research">IBM Research</a>, and was also an adjunct professor of physics at <a href="/wiki/Yale_University" title="Yale University">Yale University</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gutzwiller was born on October 12, 1925, in the <a href="/wiki/Switzerland" title="Switzerland">Swiss</a> city of <a href="/wiki/Basel" title="Basel">Basel</a>. He completed a Diploma degree from <a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a>, where he studied quantum physics under <a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Wolfgang Pauli</a>. He then went to the <a href="/wiki/University_of_Kansas" title="University of Kansas">University of Kansas</a> and completed a <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">Ph.D</a> under <a href="/wiki/Max_Dresden" title="Max Dresden">Max Dresden</a>. After graduation, he worked on microwave engineering for <a href="/wiki/Brown,_Boveri_%26_Cie" title="Brown, Boveri & Cie">Brown, Boveri & Cie</a>, on geophysics for <a href="/wiki/Royal_Dutch_Shell" class="mw-redirect" title="Royal Dutch Shell">Shell Oil</a>, and eventually for IBM Research in Switzerland, New York City, and Yorktown Heights, until his retirement in 1993. He also held temporary teaching appointments at <a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a>, ETH Zurich, <a href="/wiki/University_of_Paris-Sud" class="mw-redirect" title="University of Paris-Sud">Paris-Orsay</a>, and <a href="/wiki/Stockholm_University" title="Stockholm University">Stockholm</a>. He was Vice Chair for the Committee on Mathematical Physics, of the <a href="/wiki/International_Union_of_Pure_and_Applied_Physics" title="International Union of Pure and Applied Physics">International Union of Pure and Applied Physics</a>, from 1987 to 1993. He joined Yale University as adjunct professor in 1993, retaining the position until his retirement.<sup id="cite_ref-acp_1-2" class="reference"><a href="#cite_note-acp-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Scientific_work">Scientific work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=2" title="Edit section: Scientific work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gutzwiller formulated the <a href="/w/index.php?title=Gutzwiller_approximation&action=edit&redlink=1" class="new" title="Gutzwiller approximation (page does not exist)">Gutzwiller approximation</a> for describing electrons with strong local interactions in terms of the Gutzwiller wave function, composed of a simple many-electron wave function acted on by a correlation operator ("Gutzwiller projection"). He was also the first to investigate the relationship between classical and quantum mechanics in chaotic systems. In that context, he developed the Gutzwiller trace formula, the main result of periodic orbit theory, which gives a recipe for computing spectra from periodic orbits of a system. He is the author of the classic monograph on the subject, <i>Chaos in Classical and Quantum Mechanics</i> (1990). </p><p>Gutzwiller is also known for finding novel solutions to mathematical problems in field theory, wave propagation, crystal physics, and celestial mechanics. In appreciation of his contributions to theoretical physics, the <a href="/wiki/Max_Planck_Institute_for_the_Physics_of_Complex_Systems" title="Max Planck Institute for the Physics of Complex Systems">Max Planck Institute for the Physics of Complex Systems</a> (MPIPKS) annually awards the Martin Gutzwiller Fellowship to acknowledge and promote exceptional research in this field.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Book_collecting">Book collecting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=3" title="Edit section: Book collecting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gutzwiller had an avid interest in the <a href="/wiki/History_of_science" title="History of science">history of science</a>. He eventually acquired a valuable collection of <a href="/wiki/Book_collecting" title="Book collecting">rare books</a> on astronomy and mechanics. Shortly after his death, his collection was auctioned at <a href="/wiki/Swann_Galleries" title="Swann Galleries">Swann Galleries</a>, in New York City. The auction took place on April 3, 2014, and raised a total of US$341,788.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Honors">Honors</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=4" title="Edit section: Honors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Fellow of <a href="/wiki/National_Academies_of_Science" class="mw-redirect" title="National Academies of Science">National Academies of Science</a> in 1992</li> <li>Fellow of <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a> in 1993 <sup id="cite_ref-acp_1-3" class="reference"><a href="#cite_note-acp-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li>Fellow of <a href="/wiki/American_Physical_Society" title="American Physical Society">American Physical Society</a></li> <li><a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize for Mathematical Physics</a> in 1993 <sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Max_Planck_medal" class="mw-redirect" title="Max Planck medal">Max Planck medal</a> in 2003</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-acp-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-acp_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-acp_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-acp_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-acp_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20141011232202/http://www.aip.org/history/acap/biographies/bio.jsp?gutzwillerm">"Array of Contemporary American Physicists"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.aip.org/history/acap/biographies/bio.jsp?gutzwillerm">the original</a> on 11 October 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Array+of+Contemporary+American+Physicists&rft_id=http%3A%2F%2Fwww.aip.org%2Fhistory%2Facap%2Fbiographies%2Fbio.jsp%3Fgutzwillerm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMartin+Gutzwiller" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.nasonline.org/member-directory/deceased-members/10815.html">Directory entry</a>, National Academy of Sciences</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mpipks-dresden.mpg.de/pages/forschung/forschung_gutzwiller.html">"Martin Gutzwiller Fellowship"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Martin+Gutzwiller+Fellowship&rft_id=http%3A%2F%2Fwww.mpipks-dresden.mpg.de%2Fpages%2Fforschung%2Fforschung_gutzwiller.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMartin+Gutzwiller" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.americanaexchange.com/auctions/7167?id=7167">Auction Report</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140519221700/http://www.americanaexchange.com/auctions/7167?id=7167">Archived</a> 2014-05-19 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Americana Exchange</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.aps.org/programs/honors/prizes/prizerecipient.cfm?first_nm=Martin&last_nm=Gutzwiller&year=1993">"1993 Dannie Heineman Prize for Mathematical Physics Recipient"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=1993+Dannie+Heineman+Prize+for+Mathematical+Physics+Recipient&rft_id=http%3A%2F%2Fwww.aps.org%2Fprograms%2Fhonors%2Fprizes%2Fprizerecipient.cfm%3Ffirst_nm%3DMartin%26last_nm%3DGutzwiller%26year%3D1993&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMartin+Gutzwiller" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Martin_Gutzwiller&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=fnO3XYYpU54C&q=Martin+Gutzwiller">Chaos in classical and quantum mechanics by Martin C. Gutzwiller 1990</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaeriswylBerryVollhardt2014" class="citation journal cs1">Baeriswyl, Dionys; Berry, Michael; Vollhardt, Dieter (2014). <a rel="nofollow" class="external text" href="https://opus.bibliothek.uni-augsburg.de/opus4/files/93532/93532.pdf">"Martin Charles Gutzwiller"</a> <span class="cs1-format">(PDF)</span>. <i>Physics Today</i>. <b>67</b> (6): 60. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014PhT....67f..60B">2014PhT....67f..60B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2FPT.3.2426">10.1063/PT.3.2426</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Martin+Charles+Gutzwiller&rft.volume=67&rft.issue=6&rft.pages=60&rft.date=2014&rft_id=info%3Adoi%2F10.1063%2FPT.3.2426&rft_id=info%3Abibcode%2F2014PhT....67f..60B&rft.aulast=Baeriswyl&rft.aufirst=Dionys&rft.au=Berry%2C+Michael&rft.au=Vollhardt%2C+Dieter&rft_id=https%3A%2F%2Fopus.bibliothek.uni-augsburg.de%2Fopus4%2Ffiles%2F93532%2F93532.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMartin+Gutzwiller" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/gutzwiller-martin.pdf">M. V. Berry and D. Baeriswyl, "Martin C. Gutzwiller", Biographical Memoirs of the National Academy of Sciences (2016)</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · 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.navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Chaos_theory" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chaos_theory" title="Template:Chaos theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chaos_theory" title="Template talk:Chaos theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chaos_theory" title="Special:EditPage/Template:Chaos theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chaos_theory" style="font-size:114%;margin:0 4em"><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Core" scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Core</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attractor" title="Attractor">Attractor</a></li> <li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Limit_set" title="Limit set">Limit set</a></li> <li><a href="/wiki/Lyapunov_exponent" title="Lyapunov exponent">Lyapunov exponent</a></li> <li><a href="/wiki/Orbit_(dynamics)" title="Orbit (dynamics)">Orbit</a></li> <li><a href="/wiki/Periodic_point" title="Periodic point">Periodic point</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anosov_diffeomorphism" title="Anosov diffeomorphism">Anosov diffeomorphism</a></li> <li><a href="/wiki/Arnold_tongue" title="Arnold tongue">Arnold tongue</a></li> <li><a href="/wiki/Axiom_A" title="Axiom A">axiom A dynamical system</a></li> <li><a href="/wiki/Bifurcation_diagram" title="Bifurcation diagram">Bifurcation diagram</a></li> <li><a href="/wiki/Box-counting_dimension" class="mw-redirect" title="Box-counting dimension">Box-counting dimension</a></li> <li><a href="/wiki/Correlation_dimension" title="Correlation dimension">Correlation dimension</a></li> <li><a href="/wiki/Conservative_system" title="Conservative system">Conservative system</a></li> <li><a href="/wiki/Ergodicity" title="Ergodicity">Ergodicity</a></li> <li><a href="/wiki/False_nearest_neighbors" class="mw-redirect" title="False nearest neighbors">False nearest neighbors</a></li> <li><a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff dimension</a></li> <li><a href="/wiki/Invariant_measure" title="Invariant measure">Invariant measure</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov stability</a></li> <li><a href="/wiki/Measure-preserving_dynamical_system" title="Measure-preserving dynamical system">Measure-preserving dynamical system</a></li> <li><a href="/wiki/Mixing_(mathematics)" title="Mixing (mathematics)">Mixing</a></li> <li><a href="/wiki/Poincar%C3%A9_section" class="mw-redirect" title="Poincaré section">Poincaré section</a></li> <li><a href="/wiki/Recurrence_plot" title="Recurrence plot">Recurrence plot</a></li> <li><a href="/wiki/SRB_measure" class="mw-redirect" title="SRB measure">SRB measure</a></li> <li><a href="/wiki/Stable_manifold" title="Stable manifold">Stable manifold</a></li> <li><a href="/wiki/Topological_conjugacy" title="Topological conjugacy">Topological conjugacy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Theorems</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ergodic_theory#Ergodic_theorems" title="Ergodic theory">Ergodic theorem</a></li> <li><a href="/wiki/Liouville%27s_theorem_(Hamiltonian)" title="Liouville's theorem (Hamiltonian)">Liouville's theorem</a></li> <li><a href="/wiki/Krylov%E2%80%93Bogolyubov_theorem" title="Krylov–Bogolyubov theorem">Krylov–Bogolyubov theorem</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Bendixson_theorem" title="Poincaré–Bendixson theorem">Poincaré–Bendixson theorem</a></li> <li><a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a></li> <li><a href="/wiki/Stable_manifold_theorem" title="Stable manifold theorem">Stable manifold theorem</a></li> <li><a href="/wiki/Takens%27s_theorem" title="Takens's theorem">Takens's theorem</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:C%C3%B4ne_textileII.png" class="mw-file-description" title="Conus textile shell"><img alt="Conus textile shell" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/100px-C%C3%B4ne_textileII.png" decoding="async" width="100" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/150px-C%C3%B4ne_textileII.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/200px-C%C3%B4ne_textileII.png 2x" data-file-width="2344" data-file-height="4211" /></a></span> <p><br /> </p> <span typeof="mw:File"><a href="/wiki/File:Circle_map_poincare_recurrence.jpeg" class="mw-file-description" title="Circle map with black Arnold tongues"><img alt="Circle map with black Arnold tongues" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/100px-Circle_map_poincare_recurrence.jpeg" decoding="async" width="100" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/150px-Circle_map_poincare_recurrence.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/200px-Circle_map_poincare_recurrence.jpeg 2x" data-file-width="450" data-file-height="900" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theoretical<br />branches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation theory</a></li> <li><a href="/wiki/Control_of_chaos" title="Control of chaos">Control of chaos</a></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a></li> <li><a href="/wiki/Ergodic_theory" title="Ergodic theory">Ergodic theory</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Stability_theory" title="Stability theory">Stability theory</a></li> <li><a href="/wiki/Synchronization_of_chaos" title="Synchronization of chaos">Synchronization of chaos</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaotic<br />maps (<a href="/wiki/List_of_chaotic_maps" title="List of chaotic maps">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Discrete</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arnold%27s_cat_map" title="Arnold's cat map">Arnold's cat map</a></li> <li><a href="/wiki/Baker%27s_map" title="Baker's map">Baker's map</a></li> <li><a href="/wiki/Complex_quadratic_polynomial" title="Complex quadratic polynomial">Complex quadratic map</a></li> <li><a href="/wiki/Coupled_map_lattice" title="Coupled map lattice">Coupled map lattice</a></li> <li><a href="/wiki/Duffing_map" title="Duffing map">Duffing map</a></li> <li><a href="/wiki/Dyadic_transformation" title="Dyadic transformation">Dyadic transformation</a></li> <li><a href="/wiki/Dynamical_billiards" title="Dynamical billiards">Dynamical billiards</a> <ul><li><a href="/wiki/Outer_billiards" title="Outer billiards">outer</a></li></ul></li> <li><a href="/wiki/Exponential_map_(discrete_dynamical_systems)" title="Exponential map (discrete dynamical systems)">Exponential map</a></li> <li><a href="/wiki/Gauss_iterated_map" title="Gauss iterated map">Gauss map</a></li> <li><a href="/wiki/Gingerbreadman_map" title="Gingerbreadman map">Gingerbreadman map</a></li> <li><a href="/wiki/H%C3%A9non_map" title="Hénon map">Hénon map</a></li> <li><a href="/wiki/Horseshoe_map" title="Horseshoe map">Horseshoe map</a></li> <li><a href="/wiki/Ikeda_map" title="Ikeda map">Ikeda map</a></li> <li><a href="/wiki/Interval_exchange_transformation" title="Interval exchange transformation">Interval exchange map</a></li> <li><a href="/wiki/Irrational_rotation" title="Irrational rotation">Irrational rotation</a></li> <li><a href="/wiki/Kaplan%E2%80%93Yorke_map" title="Kaplan–Yorke map">Kaplan–Yorke map</a></li> <li><a href="/wiki/Langton%27s_ant" title="Langton's ant">Langton's ant</a></li> <li><a href="/wiki/Logistic_map" title="Logistic map">Logistic map</a></li> <li><a href="/wiki/Standard_map" title="Standard map">Standard map</a></li> <li><a href="/wiki/Tent_map" title="Tent map">Tent map</a></li> <li><a href="/wiki/Tinkerbell_map" title="Tinkerbell map">Tinkerbell map</a></li> <li><a href="/wiki/Zaslavskii_map" title="Zaslavskii map">Zaslavskii map</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Continuous</div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Double_scroll_attractor" class="mw-redirect" title="Double scroll attractor">Double scroll attractor</a></li> <li><a href="/wiki/Duffing_equation" title="Duffing equation">Duffing equation</a></li> <li><a href="/wiki/Lorenz_system" title="Lorenz system">Lorenz system</a></li> <li><a href="/wiki/Lotka%E2%80%93Volterra_equations" title="Lotka–Volterra equations">Lotka–Volterra equations</a></li> <li><a href="/wiki/Mackey%E2%80%93Glass_equations" title="Mackey–Glass equations">Mackey–Glass equations</a></li> <li><a href="/wiki/Rabinovich%E2%80%93Fabrikant_equations" title="Rabinovich–Fabrikant equations">Rabinovich–Fabrikant equations</a></li> <li><a href="/wiki/R%C3%B6ssler_attractor" title="Rössler attractor">Rössler attractor</a></li> <li><a href="/wiki/Three-body_problem" title="Three-body problem">Three-body problem</a></li> <li><a href="/wiki/Van_der_Pol_oscillator" title="Van der Pol oscillator">Van der Pol oscillator</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical<br />systems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chua%27s_circuit" title="Chua's circuit">Chua's circuit</a></li> <li><a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Convection</a></li> <li><a href="/wiki/Double_pendulum" title="Double pendulum">Double pendulum</a></li> <li><a href="/wiki/Elastic_pendulum" title="Elastic pendulum">Elastic pendulum</a></li> <li><a href="/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem" title="Fermi–Pasta–Ulam–Tsingou problem">FPUT problem</a></li> <li><a href="/wiki/H%C3%A9non%E2%80%93Heiles_system" title="Hénon–Heiles system">Hénon–Heiles system</a></li> <li><a href="/wiki/Kicked_rotator" title="Kicked rotator">Kicked rotator</a></li> <li><a href="/wiki/Multiscroll_attractor" title="Multiscroll attractor">Multiscroll attractor</a></li> <li><a href="/wiki/Population_dynamics" title="Population dynamics">Population dynamics</a></li> <li><a href="/wiki/Swinging_Atwood%27s_machine" title="Swinging Atwood's machine">Swinging Atwood's machine</a></li> <li><a href="/wiki/Tilt-A-Whirl" title="Tilt-A-Whirl">Tilt-A-Whirl</a></li> <li><a href="/wiki/Weather_forecasting" title="Weather forecasting">Weather</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaos<br />theorists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Michael_Berry_(physicist)" title="Michael Berry (physicist)">Michael Berry</a></li> <li><a href="/wiki/Rufus_Bowen" title="Rufus Bowen">Rufus Bowen</a></li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li> <li><a href="/wiki/Chen_Guanrong" title="Chen Guanrong">Chen Guanrong</a></li> <li><a href="/wiki/Leon_O._Chua" title="Leon O. Chua">Leon O. Chua</a></li> <li><a href="/wiki/Mitchell_Feigenbaum" title="Mitchell Feigenbaum">Mitchell Feigenbaum</a></li> <li><a href="/wiki/Peter_Grassberger" title="Peter Grassberger">Peter Grassberger</a></li> <li><a href="/wiki/Celso_Grebogi" title="Celso Grebogi">Celso Grebogi</a></li> <li><a class="mw-selflink selflink">Martin Gutzwiller</a></li> <li><a href="/wiki/Brosl_Hasslacher" title="Brosl Hasslacher">Brosl Hasslacher</a></li> <li><a href="/wiki/Michel_H%C3%A9non" title="Michel Hénon">Michel Hénon</a></li> <li><a href="/wiki/Svetlana_Jitomirskaya" title="Svetlana Jitomirskaya">Svetlana Jitomirskaya</a></li> <li><a href="/wiki/Bryna_Kra" title="Bryna Kra">Bryna Kra</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li> <li><a href="/wiki/Aleksandr_Lyapunov" title="Aleksandr Lyapunov">Aleksandr Lyapunov</a></li> <li><a href="/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot">Benoît Mandelbrot</a></li> <li><a href="/wiki/Hee_Oh" title="Hee Oh">Hee Oh</a></li> <li><a href="/wiki/Edward_Ott" title="Edward Ott">Edward Ott</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li><a href="/wiki/Itamar_Procaccia" title="Itamar Procaccia">Itamar Procaccia</a></li> <li><a href="/wiki/Mary_Rees" title="Mary Rees">Mary Rees</a></li> <li><a href="/wiki/Otto_R%C3%B6ssler" title="Otto Rössler">Otto Rössler</a></li> <li><a href="/wiki/David_Ruelle" title="David Ruelle">David Ruelle</a></li> <li><a href="/wiki/Caroline_Series" title="Caroline Series">Caroline Series</a></li> <li><a href="/wiki/Yakov_Sinai" title="Yakov Sinai">Yakov Sinai</a></li> <li><a href="/wiki/Oleksandr_Mykolayovych_Sharkovsky" class="mw-redirect" title="Oleksandr Mykolayovych Sharkovsky">Oleksandr Mykolayovych Sharkovsky</a></li> <li><a href="/wiki/Nina_Snaith" title="Nina Snaith">Nina Snaith</a></li> <li><a href="/wiki/Floris_Takens" title="Floris Takens">Floris Takens</a></li> <li><a href="/wiki/Audrey_Terras" title="Audrey Terras">Audrey Terras</a></li> <li><a href="/wiki/Mary_Tsingou" title="Mary Tsingou">Mary Tsingou</a></li> <li><a href="/wiki/Marcelo_Viana" title="Marcelo Viana">Marcelo Viana</a></li> <li><a href="/wiki/Amie_Wilkinson" title="Amie Wilkinson">Amie Wilkinson</a></li> <li><a href="/wiki/James_A._Yorke" title="James A. Yorke">James A. Yorke</a></li> <li><a href="/wiki/Lai-Sang_Young" title="Lai-Sang Young">Lai-Sang Young</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Butterfly_effect" title="Butterfly effect">Butterfly effect</a></li> <li><a href="/wiki/Complexity" title="Complexity">Complexity</a></li> <li><a href="/wiki/Edge_of_chaos" title="Edge of chaos">Edge of chaos</a></li> <li><a href="/wiki/Predictability" title="Predictability">Predictability</a></li> <li><a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div 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