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Peter Grassberger - Wikipedia

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class="mw-page-title-main">Peter Grassberger</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Peter Grassberger</div></th></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">17 May 1940<span style="display:none">&#160;(<span class="dtstart bday">1940-05-17</span>)</span> (age&#160;<span class="currentage"></span>84)<br /><div style="display:inline" class="birthplace"><a href="/wiki/Vienna" title="Vienna">Vienna</a>, <a href="/wiki/Nazi_Germany" title="Nazi Germany">Greater German Reich</a> (present-day <a href="/wiki/Austria" title="Austria">Austria</a>)</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/Austria" title="Austria">Austrian</a></td></tr><tr><th scope="row" class="infobox-label">Alma&#160;mater</th><td class="infobox-data"><a href="/wiki/University_of_Vienna" title="University of Vienna">University of Vienna</a></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/Physics" title="Physics">Physics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_Calgary" title="University of Calgary">University of Calgary</a>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> <a href="/wiki/Forschungszentrum_J%C3%BClich" title="Forschungszentrum Jülich">Forschungszentrum Jülich</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/Walter_Thirring" title="Walter Thirring">Walter Thirring</a>, H. Pietschmann</td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Peter Grassberger</b> (born 17 May 1940) is a retired professor who worked in statistical and <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a>. He made contributions to <a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a>, where he introduced the idea of <a href="/wiki/Correlation_dimension" title="Correlation dimension">correlation dimension</a>, a means of measuring a type of <a href="/wiki/Fractal_dimension" title="Fractal dimension">fractal dimension</a> of the <a href="/wiki/Strange_attractor" class="mw-redirect" title="Strange attractor">strange attractor</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Peter_Grassberger&amp;action=edit&amp;section=1" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Grassberger's early work focused on particle phenomenology, in particular on the formulation of formally exact equations for three-body scattering and bound state scattering (Alt-Grassberger-Sandhas equation). </p><p>While working at <a href="/wiki/CERN" title="CERN">CERN</a>, he realized that reggeon field theory can be viewed as a <a href="/wiki/Contact_process_(mathematics)" title="Contact process (mathematics)">contact process</a> in the same <a href="/wiki/Universality_class" title="Universality class">universality class</a> as <a href="/wiki/Directed_percolation" title="Directed percolation">directed percolation</a>. After making this discovery, Grassberger turned his attention to the studies of <a href="/wiki/Statistical_physics" class="mw-redirect" title="Statistical physics">statistical physics</a>, <a href="/wiki/Dynamical_systems" class="mw-redirect" title="Dynamical systems">dynamical systems</a>, sequential sampling algorithms, and <a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">complex systems</a>. His publications span a variety of topics including <a href="/wiki/Reaction-diffusion_systems" class="mw-redirect" title="Reaction-diffusion systems">reaction-diffusion systems</a>, <a href="/wiki/Cellular_automata" class="mw-redirect" title="Cellular automata">cellular automata</a>, <a href="/wiki/Fractals" class="mw-redirect" title="Fractals">fractals</a>, <a href="/wiki/Ising_model" title="Ising model">Ising model</a>, Griffiths phases, <a href="/wiki/Self-organized_criticality" title="Self-organized criticality">self-organized criticality</a>, and <a href="/wiki/Percolation" title="Percolation">percolation</a>. </p><p>He held long-term positions at the <a href="/wiki/University_of_Wuppertal" title="University of Wuppertal">University of Wuppertal</a> and at the <a href="/wiki/Forschungszentrum_J%C3%BClich" title="Forschungszentrum Jülich">Forschungszentrum Jülich</a> (Germany). Other positions that lasted between 2 years and 3 months were at <a href="/wiki/CERN" title="CERN">CERN</a>, at the Universities of Kabul, Nice, Calgary, Rome and Utrecht, the <a href="/wiki/Weizmann_Institute" class="mw-redirect" title="Weizmann Institute">Weizmann Institute</a>, 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> in Dresden, the <a href="/w/index.php?title=Istituto_nazionale_di_ottica&amp;action=edit&amp;redlink=1" class="new" title="Istituto nazionale di ottica (page does not exist)">Istituto nazionale di ottica</a><span class="noprint" style="font-size:85%; font-style: normal;">&#160;&#91;<a href="https://it.wikipedia.org/wiki/Istituto_nazionale_di_ottica" class="extiw" title="it:Istituto nazionale di ottica">it</a>&#93;</span> in Florence, and at the <a href="/wiki/Institute_for_Advanced_Studies_in_Basic_Sciences" title="Institute for Advanced Studies in Basic Sciences">Institute for Advanced Studies in Basic Sciences</a> in Zanjan, Iran. </p><p>In 2017 he received the <a href="/wiki/EPS_Statistical_and_Nonlinear_Physics_Prize" title="EPS Statistical and Nonlinear Physics Prize">EPS Statistical and Nonlinear Physics Prize</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Peter_Grassberger&amp;action=edit&amp;section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Complex_network" title="Complex network">Complex network</a></li> <li><a href="/wiki/Epidemic_models_on_lattices" title="Epidemic models on lattices">Epidemic models on lattices</a></li> <li><a href="/wiki/Mutual_information" title="Mutual information">Mutual information</a></li> <li><a href="/wiki/Forecasting_complexity" title="Forecasting complexity">Forecasting complexity</a></li> <li><a href="/wiki/Kolmogorov_entropy" class="mw-redirect" title="Kolmogorov entropy">Kolmogorov entropy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Selected_publications">Selected publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Peter_Grassberger&amp;action=edit&amp;section=3" title="Edit section: Selected publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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 id="CITEREFP._GrassbergerI._Procaccia1983" class="citation journal cs1">P. Grassberger; I. Procaccia (1983). "Measuring the strangeness of strange attractors". <i>Physica D: Nonlinear Phenomena</i>. <b>9</b> (1–2): 189–208. <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/1983PhyD....9..189G">1983PhyD....9..189G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0167-2789%2883%2990298-1">10.1016/0167-2789(83)90298-1</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Physica+D%3A+Nonlinear+Phenomena&amp;rft.atitle=Measuring+the+strangeness+of+strange+attractors&amp;rft.volume=9&amp;rft.issue=1%E2%80%932&amp;rft.pages=189-208&amp;rft.date=1983&amp;rft_id=info%3Adoi%2F10.1016%2F0167-2789%2883%2990298-1&amp;rft_id=info%3Abibcode%2F1983PhyD....9..189G&amp;rft.au=P.+Grassberger&amp;rft.au=I.+Procaccia&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerI._Procaccia1983" class="citation journal cs1">P. Grassberger; I. Procaccia (1983). "Characterization of Strange Attractors". <i>Physical Review Letters</i>. <b>50</b> (5): 346–349. <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/1983PhRvL..50..346G">1983PhRvL..50..346G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.50.346">10.1103/PhysRevLett.50.346</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Physical+Review+Letters&amp;rft.atitle=Characterization+of+Strange+Attractors&amp;rft.volume=50&amp;rft.issue=5&amp;rft.pages=346-349&amp;rft.date=1983&amp;rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.50.346&amp;rft_id=info%3Abibcode%2F1983PhRvL..50..346G&amp;rft.au=P.+Grassberger&amp;rft.au=I.+Procaccia&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFE._O._AltP._GrassbergerW._Sandhas1967" class="citation journal cs1">E. O. Alt; P. Grassberger; W. Sandhas (1967). "Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations". <i>Nuclear Physics B</i>. <b>2</b> (2): 167–180. <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/1967NuPhB...2..167A">1967NuPhB...2..167A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0550-3213%2867%2990016-8">10.1016/0550-3213(67)90016-8</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Nuclear+Physics+B&amp;rft.atitle=Reduction+of+the+three-particle+collision+problem+to+multi-channel+two-particle+Lippmann-Schwinger+equations&amp;rft.volume=2&amp;rft.issue=2&amp;rft.pages=167-180&amp;rft.date=1967&amp;rft_id=info%3Adoi%2F10.1016%2F0550-3213%2867%2990016-8&amp;rft_id=info%3Abibcode%2F1967NuPhB...2..167A&amp;rft.au=E.+O.+Alt&amp;rft.au=P.+Grassberger&amp;rft.au=W.+Sandhas&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerI._Procaccia1983" class="citation journal cs1">P. Grassberger; I. Procaccia (1983). "Estimation of the Kolmogorov entropy from a chaotic signal". <i>Physical Review A</i>. <b>28</b> (4): 2591–2593. <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/1983PhRvA..28.2591G">1983PhRvA..28.2591G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.28.2591">10.1103/PhysRevA.28.2591</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Physical+Review+A&amp;rft.atitle=Estimation+of+the+Kolmogorov+entropy+from+a+chaotic+signal&amp;rft.volume=28&amp;rft.issue=4&amp;rft.pages=2591-2593&amp;rft.date=1983&amp;rft_id=info%3Adoi%2F10.1103%2FPhysRevA.28.2591&amp;rft_id=info%3Abibcode%2F1983PhRvA..28.2591G&amp;rft.au=P.+Grassberger&amp;rft.au=I.+Procaccia&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._Grassberger1983" class="citation journal cs1">P. Grassberger (1983). "Generalized dimensions of strange attractors". <i>Physics Letters A</i>. <b>97</b> (6): 227–230. <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/1983PhLA...97..227G">1983PhLA...97..227G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0375-9601%2883%2990753-3">10.1016/0375-9601(83)90753-3</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Physics+Letters+A&amp;rft.atitle=Generalized+dimensions+of+strange+attractors&amp;rft.volume=97&amp;rft.issue=6&amp;rft.pages=227-230&amp;rft.date=1983&amp;rft_id=info%3Adoi%2F10.1016%2F0375-9601%2883%2990753-3&amp;rft_id=info%3Abibcode%2F1983PhLA...97..227G&amp;rft.au=P.+Grassberger&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerI._Procaccia1984" class="citation journal cs1">P. Grassberger; I. Procaccia (1984). "Dimensions and entropies of strange attractors from a fluctuating dynamics approach". <i>Physica D: Nonlinear Phenomena</i>. <b>13</b> (1–2): 34–54. <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/1984PhyD...13...34G">1984PhyD...13...34G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0167-2789%2884%2990269-0">10.1016/0167-2789(84)90269-0</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Physica+D%3A+Nonlinear+Phenomena&amp;rft.atitle=Dimensions+and+entropies+of+strange+attractors+from+a+fluctuating+dynamics+approach&amp;rft.volume=13&amp;rft.issue=1%E2%80%932&amp;rft.pages=34-54&amp;rft.date=1984&amp;rft_id=info%3Adoi%2F10.1016%2F0167-2789%2884%2990269-0&amp;rft_id=info%3Abibcode%2F1984PhyD...13...34G&amp;rft.au=P.+Grassberger&amp;rft.au=I.+Procaccia&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerA._de_la_Torre1979" class="citation journal cs1">P. Grassberger; A. de la Torre (1979). "Reggeon field theory (Schlögl's first model) on a lattice: Monte Carlo calculations of critical behaviour". <i>Annals of Physics</i>. <b>122</b> (2): 373–396. <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/1979AnPhy.122..373G">1979AnPhy.122..373G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0003-4916%2879%2990207-0">10.1016/0003-4916(79)90207-0</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Annals+of+Physics&amp;rft.atitle=Reggeon+field+theory+%28Schl%C3%B6gl%27s+first+model%29+on+a+lattice%3A+Monte+Carlo+calculations+of+critical+behaviour&amp;rft.volume=122&amp;rft.issue=2&amp;rft.pages=373-396&amp;rft.date=1979&amp;rft_id=info%3Adoi%2F10.1016%2F0003-4916%2879%2990207-0&amp;rft_id=info%3Abibcode%2F1979AnPhy.122..373G&amp;rft.au=P.+Grassberger&amp;rft.au=A.+de+la+Torre&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerR._BadiiA._Politi1988" class="citation journal cs1">P. Grassberger; R. Badii; A. Politi (1988). "Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors". <i>Journal of Statistical Physics</i>. <b>51</b> (1–2): 135–178. <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/1988JSP....51..135G">1988JSP....51..135G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01015324">10.1007/BF01015324</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121999076">121999076</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Journal+of+Statistical+Physics&amp;rft.atitle=Scaling+laws+for+invariant+measures+on+hyperbolic+and+nonhyperbolic+atractors&amp;rft.volume=51&amp;rft.issue=1%E2%80%932&amp;rft.pages=135-178&amp;rft.date=1988&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121999076%23id-name%3DS2CID&amp;rft_id=info%3Adoi%2F10.1007%2FBF01015324&amp;rft_id=info%3Abibcode%2F1988JSP....51..135G&amp;rft.au=P.+Grassberger&amp;rft.au=R.+Badii&amp;rft.au=A.+Politi&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._Grassberger1982" class="citation journal cs1">P. Grassberger (1982). "On phase transitions in Schlögl's second model". <i><a href="/wiki/Zeitschrift_f%C3%BCr_Physik_B" class="mw-redirect" title="Zeitschrift für Physik B">Zeitschrift für Physik B</a></i>. <b>47</b> (4): 365–374. <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/1982ZPhyB..47..365G">1982ZPhyB..47..365G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01313803">10.1007/BF01313803</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a>&#160;<a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120131896">120131896</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Zeitschrift+f%C3%BCr+Physik+B&amp;rft.atitle=On+phase+transitions+in+Schl%C3%B6gl%27s+second+model&amp;rft.volume=47&amp;rft.issue=4&amp;rft.pages=365-374&amp;rft.date=1982&amp;rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120131896%23id-name%3DS2CID&amp;rft_id=info%3Adoi%2F10.1007%2FBF01313803&amp;rft_id=info%3Abibcode%2F1982ZPhyB..47..365G&amp;rft.au=P.+Grassberger&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._GrassbergerI._Procaccia1982" class="citation journal cs1">P. Grassberger; I. Procaccia (1982). <a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.443832">"The long time properties of diffusion in a medium with static traps"</a>. <i>J. Chem. Phys</i>. <b>77</b> (12): 6281–6284. <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/1982JChPh..77.6281G">1982JChPh..77.6281G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.443832">10.1063/1.443832</a></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=J.+Chem.+Phys.&amp;rft.atitle=The+long+time+properties+of+diffusion+in+a+medium+with+static+traps&amp;rft.volume=77&amp;rft.issue=12&amp;rft.pages=6281-6284&amp;rft.date=1982&amp;rft_id=info%3Adoi%2F10.1063%2F1.443832&amp;rft_id=info%3Abibcode%2F1982JChPh..77.6281G&amp;rft.au=P.+Grassberger&amp;rft.au=I.+Procaccia&amp;rft_id=https%3A%2F%2Fdoi.org%2F10.1063%252F1.443832&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ.G._FosterD.V._FosterP._GrassbergerM._Paczuski2009" class="citation journal cs1">J.G. Foster; D.V. Foster; P. Grassberger; <a href="/wiki/Maya_Paczuski" title="Maya Paczuski">M. Paczuski</a> (2009). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2890716">"Edge Direction and the Structure of Networks"</a>. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. <b>107</b> (24): 10815–10820. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0908.4288">0908.4288</a></span>. <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/2010PNAS..10710815F">2010PNAS..10710815F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.0912671107">10.1073/pnas.0912671107</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a>&#160;<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2890716">2890716</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a>&#160;<a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20505119">20505119</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&amp;rft.atitle=Edge+Direction+and+the+Structure+of+Networks&amp;rft.volume=107&amp;rft.issue=24&amp;rft.pages=10815-10820&amp;rft.date=2009&amp;rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2890716%23id-name%3DPMC&amp;rft_id=info%3Abibcode%2F2010PNAS..10710815F&amp;rft_id=info%3Aarxiv%2F0908.4288&amp;rft_id=info%3Apmid%2F20505119&amp;rft_id=info%3Adoi%2F10.1073%2Fpnas.0912671107&amp;rft.au=J.G.+Foster&amp;rft.au=D.V.+Foster&amp;rft.au=P.+Grassberger&amp;rft.au=M.+Paczuski&amp;rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2890716&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></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=Peter_Grassberger&amp;action=edit&amp;section=4" 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-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</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="https://web.archive.org/web/20180626054613/http://www.ucalgary.ca/complexity/people/faculty/peter">"Peter Grassberger | Complexity Science Group | University of Calgary"</a>. 26 June 2018. Archived from <a rel="nofollow" class="external text" href="http://www.ucalgary.ca/complexity/people/faculty/peter">the original</a> on 26 June 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">18 November</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Peter+Grassberger+%7C+Complexity+Science+Group+%7C+University+of+Calgary&amp;rft.date=2018-06-26&amp;rft_id=http%3A%2F%2Fwww.ucalgary.ca%2Fcomplexity%2Fpeople%2Ffaculty%2Fpeter&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" 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"><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.eps.org/resource/group/b4bdd358-5b5f-403d-b81e-f906bf57f87a/long-citation.pdf">"SNPD Prizes 2017"</a> <span class="cs1-format">(PDF)</span>. <i>eps.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">18 November</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=eps.org&amp;rft.atitle=SNPD+Prizes+2017&amp;rft_id=http%3A%2F%2Fwww.eps.org%2Fresource%2Fgroup%2Fb4bdd358-5b5f-403d-b81e-f906bf57f87a%2Flong-citation.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3APeter+Grassberger" class="Z3988"></span></span> </li> </ol></div></div> <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 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.asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}</style><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span style="vertical-align:middle; background:transparent; color:inherit;"><span class="mw-image-border" typeof="mw:File"><a href="/wiki/File:Flag_of_Austria.svg" class="mw-file-description"><img alt="Flag of Austria" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/40px-Flag_of_Austria.svg.png" decoding="async" width="40" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/60px-Flag_of_Austria.svg.png 1.5x, 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