## 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.## References

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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