Mixing-like properties for some generic and robust dynamics

We show that the whole manifold is a homoclinic class for an open and dense subset of the set of robustly transitive diffeomorphisms far away from homoclinic tangencies. In particular, using the results from Abdenur and Crovisier, we obtain that every diffeomorphism in this subset is robustly topolo...

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Bibliographic Details
Published in:Nonlinearity 2015-11, Vol.28 (11), p.4103-4115
Main Authors: Arbieto, Alexander, Catalan, Thiago, Santiago, Bruno
Format: Article
Language:English
Subjects:
Bernoulli measures
Dynamic mechanical properties
homoclinic classes
homoclinic tangency
Invariants
Manifolds
Nonlinear dynamics
Nonlinearity
partially hyperbolic diffeomorphisms
robustly transitive diffemorphisms
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Summary:We show that the whole manifold is a homoclinic class for an open and dense subset of the set of robustly transitive diffeomorphisms far away from homoclinic tangencies. In particular, using the results from Abdenur and Crovisier, we obtain that every diffeomorphism in this subset is robustly topologically mixing. We also show that the set of Bernoulli measures of an isolated topologically mixing homoclinic class of a generic diffeomorphism is a dense subset of the set of invariant measures supported on the class.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/11/4103