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Upper bounds on measure-theoretic tail entropy for dominated splittings

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior Ergodic theory

Published online by Cambridge University Press:  26 February 2019

YONGLUO CAO ,
GANG LIAO  and
ZHIYUAN YOU
YONGLUO CAO
Affiliation:
Department of Mathematics, East China Normal University, Shanghai200062, China email ylcao@suda.edu.cn School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China email lg@suda.edu.cn, suzhouyou@qq.com
GANG LIAO
Affiliation:
School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China email lg@suda.edu.cn, suzhouyou@qq.com
ZHIYUAN YOU
Affiliation:
School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China email lg@suda.edu.cn, suzhouyou@qq.com
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Abstract

For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy in various settings with domination.

Keywords

measure-theoretic tail entropydominated splittingupper semi-continuity

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 37D30: Partially hyperbolic systems and dominated splittings 37C40: Smooth ergodic theory, invariant measures

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 9 , September 2020 , pp. 2305 - 2316
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Copyright
© Cambridge University Press, 2019

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