New Criteria of Generic Hyperbolicity based on Periodic Points

Details New Criteria of Generic Hyperbolicity based on Periodic Points New Criteria of Generic Hyperbolicity based on Periodic Points

2009-06-12

arxiv.org/abs/0906.2240v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

We prove that, if a mild condition on the hyperbolicity of the periodic points holds for any diffeomorphism in a residual subset of a $C^1$-open set $\SU$, then such set $\SU$ exhibits a residual subset $\SA$ of Axiom A diffeomorphisms. We also prove an analogous result for nonsingular endomorphisms: if a mild expanding condition holds for the periodic set of local diffeomorphisms belonging in a residual subset of a $C^1$ open set $\SU$, then $\SU$ exhibits an open and dense subset of expanding maps. For this last result we use noninvertible versions of Ergodic Closing Lemma that we have proved (see ArXiv 0906.2031)

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