Super-exponential growth of the number of periodic orbits inside homoclinic classes

Christian Bonatti; Lorenzo J. Díaz; Todd Fisher

doi:10.3934/dcds.2008.20.589

Article Contents

2008, Volume 20, Issue 3: 589-604. Doi: 10.3934/dcds.2008.20.589

This issue Previous Article Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$ Next Article Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension

Super-exponential growth of the number of periodic orbits inside homoclinic classes

1.
Université de Bourgogne, Laboratoire de Topologie, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex
2.
Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro
3.
Department of Mathematics, Brigham Young University, Provo, UT 84602

Received: December 31, 2006

Revised: July 31, 2007

Published: August 2008

Abstract Related Papers Cited by

Abstract

We show that there is a residual subset $\S (M)$ of Diff$^1$ (M) such that, for every $f\in \S(M)$, any homoclinic class of $f$ containing periodic saddles $p$ and $q$ of indices $\alpha$ and $\beta$ respectively, where $\alpha< \beta$, has superexponential growth of the number of periodic points inside the homoclinic class. Furthermore, it is shown that the super-exponential growth occurs for hyperbolic periodic points of index $\gamma$ inside the homoclinic class for every $\gamma\in[\alpha,\beta]$.

Keywords:

Mathematics Subject Classification: Primary: 37C05, 37C20, 37C25, 37C29, 37D30.

Citation:

Article Metrics

HTML views() PDF downloads(92) Cited by(0)

Super-exponential growth of the number of periodic orbits inside homoclinic classes

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Super-exponential growth of the number of periodic orbits inside homoclinic classes

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content