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NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC HOMOCLINIC CLASSES

  • Dawei Yang (a1) and Jinhua Zhang (a2)

Abstract

We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak $\ast$ -topology and in entropy. For hyperbolic ergodic measures, it is a classical result of A. Katok. The novelty here is to deal with non-hyperbolic ergodic measures. As a consequence, we obtain the continuity of topological entropy.

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This work was done when J. Zhang visited Soochow University in July 2017. J. Zhang would like to thank Soochow University for hospitality. D. Yang was partially supported by NSFC 11671288 and NSFC 11790274. J. Zhang was partially supported by the ERC project 692925 NUHGD. J. Zhang is the corresponding author.

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NON-HYPERBOLIC ERGODIC MEASURES AND HORSESHOES IN PARTIALLY HYPERBOLIC HOMOCLINIC CLASSES

  • Dawei Yang (a1) and Jinhua Zhang (a2)

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