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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions
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by Masayuki Asaoka PDF
Proc. Amer. Math. Soc. 136 (2008), 677-686 Request permission

Erratum: Proc. Amer. Math. Soc. 138 (2010), 1533-1533.

Abstract:

For any manifold of dimension at least three, we give a simple construction of a hyperbolic invariant set that exhibits $C^1$-persistent homoclinic tangency. It provides an open subset of the space of $C^1$-diffeomorphisms in which generic diffeomorphisms have arbitrary given growth of the number of attracting periodic orbits and admit no symbolic extensions.
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Additional Information
  • Masayuki Asaoka
  • Affiliation: Department of Mathematics, Kyoto University, 606-8502 Kyoto, Japan
  • Email: asaoka@math.kyoto-u.ac.jp
  • Received by editor(s): October 17, 2006
  • Received by editor(s) in revised form: February 1, 2007
  • Published electronically: October 18, 2007
  • Additional Notes: The author was supported by JSPS PostDoctoral Fellowships for Research Abroad.
  • Communicated by: Jane M. Hawkins
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 677-686
  • MSC (2000): Primary 37C29; Secondary 37C20, 37B10
  • DOI: https://doi.org/10.1090/S0002-9939-07-09115-0
  • MathSciNet review: 2358509