Applications of Mañé's C^2 connecting lemma

We consider a few applications of Mañé's C^2 Connecting Lemma. These are the C^2 creation of homoclinic points associated to a basic set (i.e., isolated transitive hyperbolic set), a C^2 locally generic criterion to know whether a given point belongs to the stable set of hyperbolic homoclinic c...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2010-04, Vol.138 (4), p.1371
Main Author: Shuhei Hayashi
Format: Article
Language:English
Online Access:Get full text
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Summary:We consider a few applications of Mañé's C^2 Connecting Lemma. These are the C^2 creation of homoclinic points associated to a basic set (i.e., isolated transitive hyperbolic set), a C^2 locally generic criterion to know whether a given point belongs to the stable set of hyperbolic homoclinic classes, and that measurably hyperbolic diffeomorphisms (i.e., having the closure of supports of all invariant measures as a countable union of disjoint basic sets) are C^2 generically uniformly hyperbolic diffeomorphisms.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-09-10148-X