{"id":795,"date":"2018-10-11T15:17:10","date_gmt":"2018-10-11T18:17:10","guid":{"rendered":"http:\/\/www.cemeai.icmc.usp.br\/Reconnect\/?p=795"},"modified":"2020-07-06T12:48:31","modified_gmt":"2020-07-06T15:48:31","slug":"lift-problem-and-equilibrium-states","status":"publish","type":"post","link":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/lift-problem-and-equilibrium-states\/","title":{"rendered":"Lift problem and equilibrium states"},"content":{"rendered":"<h2 class=\"r\"><a href=\"http:\/\/buscatextual.cnpq.br\/buscatextual\/visualizacv.do?id=K4784516Y9&amp;idiomaExibicao=2\"><span style=\"color: #333399;\">Vilton Pinheiro<\/span><\/a><\/h2>\n<h3>Abstract:<\/h3>\n<p>In the first lecture we will talk about the problem of lifting a measure to an induced map. We will give a necessary and sufficient condition for a measure to be liftable as well as a condition for the lift to be ergodic and unique.<\/p>\n<p>The second lecture will be dedicated to construct induced maps well adapted to a given ergodic invariant probability with all its Lyapunov exponents being positive (expanding measure).<\/p>\n<p>Finally, in the third lecture, we will discuss about equilibrium states on the support of an ergodic invariant expanding probability. In particular, (1) \u00a0we will show that Viana maps have one and only one probability maximizing their entropy and (2) we will analyze the existence and uniqueness of the equilibrium states for H\u00f6lder potentials at high temperature.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vilton Pinheiro Abstract: In the first lecture we will talk about the problem of lifting a measure to an induced map. We will give a necessary and sufficient condition for a measure to be liftable as well as a condition for the lift to be ergodic and unique. The second lecture will be dedicated to [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-795","post","type-post","status-publish","format-standard","hentry","category-sem-categoria"],"_links":{"self":[{"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/posts\/795","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/comments?post=795"}],"version-history":[{"count":2,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/posts\/795\/revisions"}],"predecessor-version":[{"id":797,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/posts\/795\/revisions\/797"}],"wp:attachment":[{"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/media?parent=795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/categories?post=795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cemeai.icmc.usp.br\/Reconnect\/wp-json\/wp\/v2\/tags?post=795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}