Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems

Zheng  Yin; Ercai  Chen

doi:10.3934/dcds.2016085

Article Contents

2016, Volume 36, Issue 11: 6581-6597. Doi: 10.3934/dcds.2016085

This issue Previous Article Longtime behavior of the semilinear wave equation with gentle dissipation Next Article Weakly hyperbolic invariant tori for two dimensional quasiperiodically forced maps in a degenerate case

Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems

Zheng Yin^1, and
Ercai Chen^2,

1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu
2.
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, Jiangsu

Received: October 31, 2015

Revised: May 31, 2016

Published: May 2017

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Abstract

This article is devoted to the study of the irregular sets of Birkhoff averages in some nonuniformly hyperbolic systems via Pesin theory. Particularly, we give a conditional variational principle for the topological entropy of the irregular sets. Our result can be applied (i) to the diffeomorphisms on surfaces, (ii) to the nonuniformly hyperbolic diffeomorphisms described by Katok.

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Mathematics Subject Classification: Primary: 37B40, 37C45; Secondary: 37D25.

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