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

Dawei Yang; Jinhua Zhang

doi:10.1017/S1474748018000579

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

Dawei Yang
, Jinhua Zhang

科研成果: 期刊稿件 › 文章 › 同行评审

13 引用（Scopus）

摘要

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∗-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.

源语言	英语
页（从-至）	1765-1792
页数	28
期刊	Journal of the Institute of Mathematics of Jussieu
卷	19
期	5
DOI	https://doi.org/10.1017/S1474748018000579
出版状态	已出版 - 2020
已对外发布	是

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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∗-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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AU - Zhang, Jinhua

N1 - Publisher Copyright: © Cambridge University Press 2019

PY - 2020

Y1 - 2020

N2 - 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∗-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.

AB - 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∗-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.

KW - blender horseshoe

KW - entropy

KW - non-hyperbolic ergodic measure

KW - partial hyperbolicity

KW - periodic measure

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

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