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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Brazilian mathematician</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">Artur Oscar Lopes</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Foto-artur.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2c/Foto-artur.jpg" decoding="async" width="85" height="128" class="mw-file-element" data-file-width="85" data-file-height="128" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1950-10-17</span>)</span>October 17, 1950<br /><div style="display:inline" class="birthplace">Rio de Janeiro, Brazil</div></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data">Ph.D. in Mathematics from IMPA (1977)</td></tr><tr><th scope="row" class="infobox-label">Occupation(s)</th><td class="infobox-data role">Writer, Mathematician</td></tr><tr><th scope="row" class="infobox-label">Employer(s)</th><td class="infobox-data org">UFRGS, Porto Alegre</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data">Work on dynamical systems and ergodic theory</td></tr><tr><th scope="row" class="infobox-label"><span style="white-space:nowrap;">Notable work</span></th><td class="infobox-data"> <ul><li>Tópicos de Mecânica Clássica</li> <li>Cálculo Tensorial</li> <li>Teoria dos Corpos</li> <li>Equações Diferenciais Ordinárias</li></ul> </td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data">Brazil's National Order of Scientific Merit in mathematics</td></tr></tbody></table> <p><b>Artur Oscar Lopes</b> (born 17 October 1950 in the city of <a href="/wiki/Rio_de_Janeiro" title="Rio de Janeiro">Rio de Janeiro</a>) is a <a href="/wiki/Brazilians" title="Brazilians">Brazilian</a> <a href="/wiki/Writer" title="Writer">writer</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> working on <a href="/wiki/Dynamical_system" title="Dynamical system">dynamical systems</a> and <a href="/wiki/Ergodic_theory" title="Ergodic theory">ergodic theory</a>.<sup id="cite_ref-ABC_2-0" class="reference"><a href="#cite_note-ABC-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> He is a professor at <a href="/wiki/Universidade_Federal_do_Rio_Grande_do_Sul" class="mw-redirect" title="Universidade Federal do Rio Grande do Sul">UFRGS</a>, <a href="/wiki/Porto_Alegre" title="Porto Alegre">Porto Alegre</a>.<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><p>He earned his Ph.D. from the <a href="/wiki/Instituto_Nacional_de_Matem%C3%A1tica_Pura_e_Aplicada" title="Instituto Nacional de Matemática Pura e Aplicada">IMPA</a> in 1977 under the supervision of <a href="/wiki/Jacob_Palis" title="Jacob Palis">Jacob Palis</a>.<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><p>He is a recipient of <a href="/wiki/National_Order_of_Scientific_Merit_(Brazil)" class="mw-redirect" title="National Order of Scientific Merit (Brazil)">Brazil's National Order of Scientific Merit</a> in mathematics.<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> Since 2007 he has been a member of the <a href="/wiki/Brazilian_Academy_of_Sciences" title="Brazilian Academy of Sciences">Brazilian Academy of Sciences</a>.<sup id="cite_ref-ABC_2-1" class="reference"><a href="#cite_note-ABC-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>He is the author of the textbooks <i><span title="Portuguese-language text"><i lang="pt">Tópicos de Mecânica Clássica</i></span></i>, <i><span title="Portuguese-language text"><i lang="pt">Cálculo Tensorial</i></span></i>, <i><span title="Portuguese-language text"><i lang="pt">Teoria dos Corpos</i></span></i>, and <i><span title="Portuguese-language text"><i lang="pt">Equações Diferenciais Ordinárias</i></span></i>. </p> <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=Artur_Oscar_Lopes&action=edit&section=1" title="Edit section: Selected publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>with A. Freire and <a href="/wiki/Ricardo_Ma%C3%B1%C3%A9" title="Ricardo Mañé">R. Mañé</a>: <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="CITEREFFreireLopesMañé1983" class="citation cs2">Freire, Alexandre; Lopes, Artur; Mañé, Ricardo (March 1983), "An invariant measure for rational maps", <i><a href="/wiki/Bulletin_of_the_Brazilian_Mathematical_Society" title="Bulletin of the Brazilian Mathematical Society">Bulletin of the Brazilian Mathematical Society</a></i>, <b>14</b>: 45–62, <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/10.1007%2FBF02584744">10.1007/BF02584744</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+Brazilian+Mathematical+Society&rft.atitle=An+invariant+measure+for+rational+maps&rft.volume=14&rft.pages=45-62&rft.date=1983-03&rft_id=info%3Adoi%2F10.1007%2FBF02584744&rft.aulast=Freire&rft.aufirst=Alexandre&rft.au=Lopes%2C+Artur&rft.au=Ma%C3%B1%C3%A9%2C+Ricardo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLopes1989" class="citation cs2">Lopes, Artur O. (1989), "The dimension spectrum of the maximal measure", <i><a href="/wiki/SIAM_Journal_on_Mathematical_Analysis" class="mw-redirect" title="SIAM Journal on Mathematical Analysis">SIAM Journal on Mathematical Analysis</a></i>, <b>20</b> (5): 1243–1254, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F0520081">10.1137/0520081</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Journal+on+Mathematical+Analysis&rft.atitle=The+dimension+spectrum+of+the+maximal+measure&rft.volume=20&rft.issue=5&rft.pages=1243-1254&rft.date=1989&rft_id=info%3Adoi%2F10.1137%2F0520081&rft.aulast=Lopes&rft.aufirst=Artur+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" class="Z3988"></span></li> <li>with G. Contreras and Ph. Thieullen: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFContrerasLopesThieullen2001" class="citation cs2">Contreras, G.; Lopes, A. O.; Thieullen, PH. (October 2001), "Lyapunov minimizing measures for expanding maps of the circle", <i><a href="/wiki/Ergodic_Theory_and_Dynamical_Systems" title="Ergodic Theory and Dynamical Systems">Ergodic Theory and Dynamical Systems</a></i>, <b>21</b> (5): 1379–1409, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0143385701001663">10.1017/S0143385701001663</a>, <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10183%2F27431">10183/27431</a></span>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37683359">37683359</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Ergodic+Theory+and+Dynamical+Systems&rft.atitle=Lyapunov+minimizing+measures+for+expanding+maps+of+the+circle&rft.volume=21&rft.issue=5&rft.pages=1379-1409&rft.date=2001-10&rft_id=info%3Ahdl%2F10183%2F27431&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37683359%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1017%2FS0143385701001663&rft.aulast=Contreras&rft.aufirst=G.&rft.au=Lopes%2C+A.+O.&rft.au=Thieullen%2C+PH.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLopes1993" class="citation cs2">Lopes, A.O. (October 1993), "The zeta function, non-differentiability of pressure, and the critical exponent of transition", <i><a href="/wiki/Advances_in_Mathematics" title="Advances in Mathematics">Advances in Mathematics</a></i>, <b>101</b> (2): 133–165, <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/10.1006%2Faima.1993.1045">10.1006/aima.1993.1045</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advances+in+Mathematics&rft.atitle=The+zeta+function%2C+non-differentiability+of+pressure%2C+and+the+critical+exponent+of+transition&rft.volume=101&rft.issue=2&rft.pages=133-165&rft.date=1993-10&rft_id=info%3Adoi%2F10.1006%2Faima.1993.1045&rft.aulast=Lopes&rft.aufirst=A.O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" 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=Artur_Oscar_Lopes&action=edit&section=2" 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://www1.folha.uol.com.br/fsp/ilustrad/fq2208200715.htm">"Folha de S.Paulo - "Desengano" vence Jabuti em "romance" - 22/08/2007"</a>. <i>www1.folha.uol.com.br</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-01-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www1.folha.uol.com.br&rft.atitle=Folha+de+S.Paulo+-+%22Desengano%22+vence+Jabuti+em+%22romance%22+-+22%2F08%2F2007&rft_id=https%3A%2F%2Fwww1.folha.uol.com.br%2Ffsp%2Filustrad%2Ffq2208200715.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" class="Z3988"></span></span> </li> <li id="cite_note-ABC-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-ABC_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ABC_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20151208055227/http://www.abc.org.br/~aol">Academia Brasileira de Ciências – Artur Oscar Lopes</a></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://mat.ufrgs.br/~alopes/">"Artur Oscar Lopes"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Artur+Oscar+Lopes&rft_id=http%3A%2F%2Fmat.ufrgs.br%2F~alopes%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" 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="https://mathgenealogy.org/id.php?id=53020">Artur Oscar Lopes</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></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="https://archive.today/20150418134045/http://www.mct.gov.br/index.php/content/view/11199/11199.html?nome=&area=Ci%EAncias+Matem%E1ticas&classificacao=&categoria=vivo">"Portal do Ministério da Ciência, Tecnologia e Inovação"</a>. <i>mct.gov.br</i>. Archived from <a rel="nofollow" class="external text" href="http://www.mct.gov.br/index.php/content/view/11199/11199.html?nome=&area=Ci%EAncias+Matem%E1ticas&classificacao=&categoria=vivo">the original</a> on 2015-04-18<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-05-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mct.gov.br&rft.atitle=Portal+do+Minist%C3%A9rio+da+Ci%C3%AAncia%2C+Tecnologia+e+Inova%C3%A7%C3%A3o&rft_id=http%3A%2F%2Fwww.mct.gov.br%2Findex.php%2Fcontent%2Fview%2F11199%2F11199.html%3Fnome%3D%26area%3DCi%25EAncias%2BMatem%25E1ticas%26classificacao%3D%26categoria%3Dvivo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtur+Oscar+Lopes" class="Z3988"></span></span> </li> </ol></div></div> <p><br /> </p> <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 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href="https://mathscinet.ams.org/mathscinet/MRAuthorID/115730">MathSciNet</a></span></li></ul></div></td></tr></tbody></table></div> <p><br /> </p> <style data-mw-deduplicate="TemplateStyles:r1012311289">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .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_Brazil.svg" class="mw-file-description"><img alt="Flag of Brazil" 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