dc.contributorPablo Daniel Carrasco Correa
dc.contributorhttp://lattes.cnpq.br/8094045499632252
dc.contributorSônia Pinto de Carvalho
dc.contributorhttp://lattes.cnpq.br/6695125616195750
dc.contributorChristian Rodrigues
dc.contributorMarcelo Richard Hilário
dc.contributorRenato Feres
dc.contributorRenato Soares dos Santos
dc.contributorSilvie Marie Kamphorst
dc.creatorTúlio Vales Deslandes Ferreira
dc.date.accessioned2021-07-07T01:42:18Z
dc.date.accessioned2022-10-03T23:34:36Z
dc.date.available2021-07-07T01:42:18Z
dc.date.available2022-10-03T23:34:36Z
dc.date.created2021-07-07T01:42:18Z
dc.date.issued2021-04-14
dc.identifierhttp://hdl.handle.net/1843/36670
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/3824811
dc.description.abstractIn the first part of the thesis, we work with the random walk in a random environment determined by a partially hyperbolic diffeomorphism. In this work, we found necessary and sufficient conditions for the existence of a stationary measure for this random process, recurrence and we made a study of the dynamics of this process. As a particular case, we studied the time 1 of the geodesic flow in a compact hyperbolic manifold. In addition, we obtained a law of large numbers and a Central Limit Theorem. In the second part of the thesis we defined a random billiard, with a pertur bation in the exit angles and found an invariant measure for this random billiard in general tables. We did a more detailed study in the circle and in this case we found a null Lyapunov exponent, we showed the non-ergodicity of this system and a law called Knudsen’s Strong Law. We show that under certain conditions, almost all (random) trajectory is dense at the edge of the circular table. We also introduced the concept of pseudo caustics.
dc.publisherUniversidade Federal de Minas Gerais
dc.publisherBrasil
dc.publisherICX - DEPARTAMENTO DE MATEMÁTICA
dc.publisherPrograma de Pós-Graduação em Matemática
dc.publisherUFMG
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/
dc.rightsAcesso Aberto
dc.subjectPasseio Aleatório
dc.subjectFluxo Geodésico
dc.subjectParcialmente Hiperbólico
dc.subjectBilhar Aleatório
dc.subjectExpoente de Lyapunov
dc.subjectLei Forte de Knudsen
dc.titlePasseios e bilhares: Uma incursão em sistemas dinâmicos aleatórios
dc.typeTese


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