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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2010.tde-13052010-141003
Document
Author
Full name
Marcus Augusto Bronzi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Tahzibi, Ali (President)
Apaza, Carlos Alberto Maquera
Ehrenfeld, Carlos Humberto Vasquez
Horita, Vanderlei Minori
Mendoza, Alexander Eduardo Arbieto
Title in Portuguese
Tangências homoclínicas, entropia e medidas de SRB
Keywords in Portuguese
Entropia
Medida de SRB
Tangência homoclínica
Abstract in Portuguese
Estudamos o efeito de uma tangência homoclínica na variação da entropia topológica. Provamos que um difeomorfismo com uma tangência homoclínica associada a uma peça básica com máxima entropia é um ponto de variação da entropia na topologia 'C POT. INFINITO'. Além disso, discutimos o problema variacional na topologia 'C POT.1' e apresentamos um exemplo de descontinuidade da entropia em dimensão três. Um resultado devido a Newhouse afirma que um difeomorfismo genérico sobre uma superfície com um conjunto homoclínico que contém uma tangência correspondente a um ponto periódico dissipativo, não pode ter medidas de SRB suportadas no conjunto homoclínico. Generalizamos este resultado para dimensões maiores, no caso em que a tangência homoclínica está associada com uma sela seccionalmente dissipativa
Title in English
Homoclinic tangencies, entropy and SRB measure
Keywords in English
Entropy and SRB measure
Homoclinic tangency
Abstract in English
We study the effect of a homoclinic tangency in the variation of the topological entropy. We prove that a diffeomorphism with a homoclinic tangency associated to a basic hyperbolic set with maximal entropy is a point of entropy variation in the 'C POT THE INFINITE' topology. We also discuss variational problem in 'C POT.1' topology and we show an example of discontinuity of the entropy in dimension three. A result due to Newhouse states that a generic surface diffeomorphism with a homoclinic set containing a tangency associated to a dissipative periodic point, can not have SRB (Sinai-Ruelle-Bowen) measures supported on the homoclinic set. We generalize this result to higher dimensions, in the case where the homoclinic tangency is associated to a sectionally dissipative saddle
 
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Marcus_Bronzi_Tese.pdf (570.98 Kbytes)
Publishing Date
2010-05-13
 
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