{"id":156,"date":"2017-07-11T09:39:51","date_gmt":"2017-07-11T12:39:51","guid":{"rendered":"http:\/\/www.professores.uff.br\/kocsard\/?p=156"},"modified":"2020-09-03T10:45:15","modified_gmt":"2020-09-03T13:45:15","slug":"teoria-ergodica-doutorado","status":"publish","type":"post","link":"https:\/\/www.professores.uff.br\/kocsard\/2017\/07\/11\/teoria-ergodica-doutorado\/","title":{"rendered":"Teoria Erg\u00f3dica (doutorado)"},"content":{"rendered":"<h3><strong>Programa<\/strong><\/h3>\n<p>Teorema de recorr\u00eancia de Poincar\u00e9. Indu\u00e7\u00e3o, torres e o Teorema de Kakutani-Rokhlin. Exist\u00eancia de medidas invariantes para transforma\u00e7\u00f5es cont\u00ednuas. Teoremas erg\u00f3dicos de von Neumann e Birkhoff. Teorema erg\u00f3dico sub-aditivo. Transforma\u00e7\u00f5es erg\u00f3dicas e misturadoras. Propriedades espectrais. Transforma\u00e7\u00f5es unicamente erg\u00f3dicas. Exemplos: shifts, automorfismos e transla\u00e7\u00f5es do toro. Decomposi\u00e7\u00e3o erg\u00f3dica de medidas invariantes. Fatores e extens\u00f5es. Rela\u00e7\u00f5es de equival\u00eancia entre sistemas. Entropias m\u00e9trica e topol\u00f3gica. Princ\u00edpio variacional.<\/p>\n<h3><strong>Bibliografia<\/strong><\/h3>\n<ul>\n<li>K. Oliveira e M. Viana, <em><a href=\"http:\/\/w3.impa.br\/~viana\/out\/OV3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Fundamentos da Teoria Erg\u00f3dica.<\/a><\/em> Sociedade Brasileira de Matem\u00e1tica, 2014<\/li>\n<li>M. Einsiedler and T. Ward, <em>Ergodic Theory (with a view towards Number Theory).<\/em> Graduate Texts in Mathematics, Springer Verlag, 2011.<\/li>\n<li>M. Nadkarni, <em>Basic Ergodic Theory.<\/em> Birkh\u00e4user, 1998.<\/li>\n<\/ul>\n<h3>Refer\u00eancias complementares sobre Teoria da Medida<\/h3>\n<ul>\n<li>R. Bartle, <em>The elements of integration and Lebesgue measure.<\/em> John Wiley &amp; Sons, 1995.<\/li>\n<li>V. Climenhaga and A. Katok, <em><a href=\"https:\/\/arxiv.org\/pdf\/1208.4550v1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Measure theory through dynamical eyes<\/a><\/em>, 2012.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Programa Teorema de recorr\u00eancia de Poincar\u00e9. Indu\u00e7\u00e3o, torres e o Teorema de Kakutani-Rokhlin. Exist\u00eancia de medidas invariantes para transforma\u00e7\u00f5es cont\u00ednuas. Teoremas erg\u00f3dicos de von Neumann e Birkhoff. Teorema erg\u00f3dico sub-aditivo. Transforma\u00e7\u00f5es erg\u00f3dicas e misturadoras. Propriedades espectrais. Transforma\u00e7\u00f5es unicamente erg\u00f3dicas. Exemplos: shifts, automorfismos e transla\u00e7\u00f5es do toro. Decomposi\u00e7\u00e3o erg\u00f3dica de medidas invariantes. Fatores e extens\u00f5es. Rela\u00e7\u00f5es [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[7,6],"tags":[],"class_list":["post-156","post","type-post","status-publish","format-standard","hentry","category-ementa","category-ensino"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/posts\/156","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/comments?post=156"}],"version-history":[{"count":3,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/posts\/156\/revisions"}],"predecessor-version":[{"id":331,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/posts\/156\/revisions\/331"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/media?parent=156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/categories?post=156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/kocsard\/wp-json\/wp\/v2\/tags?post=156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}