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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Applications of Mañé’s $C^2$ connecting lemma
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by Shuhei Hayashi PDF
Proc. Amer. Math. Soc. 138 (2010), 1371-1385 Request permission

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.
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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