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Hyperbolic sets exhibiting $ C^1$-persistent homoclinic tangency for higher dimensions


Author: Masayuki Asaoka
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
Published electronically: October 18, 2007
Erratum: Proc. Amer. Math. Soc. 138 (2010), 1533
MathSciNet review: 2358509
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Abstract | References | Similar Articles | Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-07-09115-0
Keywords: Newhouse phenomena, wild dynamics, symbolic extensions
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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