Applications of Mañé’s $C^2$ connecting lemma
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Abstract:
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.References
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Additional Information
- Shuhei Hayashi
- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo, Japan
- Email: shuhei@ms.u-tokyo.ac.jp
- Received by editor(s): March 15, 2009
- Received by editor(s) in revised form: July 31, 2009
- Published electronically: December 4, 2009
- Communicated by: Bryna Kra
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 1371-1385
- MSC (2010): Primary 37C20, 37C29, 37C40, 37D05, 37D20
- DOI: https://doi.org/10.1090/S0002-9939-09-10148-X
- MathSciNet review: 2578529