Hyperbolic periodic points for chain hyperbolic homoclinic classes

Wenxiang Sun; Yun Yang

doi:10.3934/dcds.2016.36.3911

Article Contents

2016, Volume 36, Issue 7: 3911-3925. Doi: 10.3934/dcds.2016.36.3911

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Hyperbolic periodic points for chain hyperbolic homoclinic classes

Wenxiang Sun^1, and
Yun Yang^2,

1.
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871
2.
School of Mathematical Sciences, Peking University, Beijing, 100871

Received: April 30, 2015

Revised: December 31, 2015

Published: May 2017

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Abstract

In this paper we establish a closing property and a hyperbolic closing property for thin trapped chain hyperbolic homoclinic classes with one dimensional center in partial hyperbolicity setting. Taking advantage of theses properties, we prove that the growth rate of the number of hyperbolic periodic points is equal to the topological entropy. We also obtain that the hyperbolic periodic measures are dense in the space of invariant measures.

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Mathematics Subject Classification: 37D30, 37D20, 37C29.

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