On $C^1$-persistently expansive homoclinic classes

Autor:	José L. Vieitez, Martín Sambarino
Rok vydání:	2006
Předmět:	Discrete mathematics Pure mathematics Mathematics::Dynamical Systems Applied Mathematics Attractor Discrete Mathematics and Combinatorics Periodic point Homoclinic orbit Diffeomorphism Invariant (mathematics) Expansive Analysis Mathematics
Zdroj:	Discrete & Continuous Dynamical Systems - A. 14:465-481
ISSN:	1553-5231
DOI:	10.3934/dcds.2006.14.465
Popis:	Let $f: M \to M$ be a diffeomorphism defined in a $d$-dimensional compact boundary-less manifold $M$. We prove that $C^1$-persistently expansive homoclinic classes $H(p)$, $p$ an $f$-hyperbolic periodic point, have a dominated splitting $E\oplus F$, $\dim(E)=\mbox{index}(p)$. Moreover, we prove that if the $H(p)$-germ of $f$ is expansive (in particular if $H(p)$ is an attractor, repeller or maximal invariant) then it is hyperbolic.
Databáze:	OpenAIRE
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