SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS

doi:10.1007/s10473-022-0211-z

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 575-587.doi: 10.1007/s10473-022-0211-z

SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS

张文达¹, 李智强²

1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

收稿日期:2020-06-13 修回日期:2021-05-21 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Zhiqiang LI,E-mail:zqli@cqu.edu.cn E-mail:zqli@cqu.edu.cn
作者简介:Wenda ZHANG,E-mail:wendazhang951@aliyun.com
基金资助:
The first author is supported by a NSFC grant (11501066) and the Department of Education in Chongqing City (KJQN201900724 and KJQN202100722) in Chongqing Jiaotong University. The second author is supported by the Chongqing Key Laboratory of Analytic Mathematics and Applications.

SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS

Wenda ZHANG¹, Zhiqiang LI²

1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2020-06-13 Revised:2021-05-21 Online:2022-04-25 Published:2022-04-22
Supported by:
The first author is supported by a NSFC grant (11501066) and the Department of Education in Chongqing City (KJQN201900724 and KJQN202100722) in Chongqing Jiaotong University. The second author is supported by the Chongqing Key Laboratory of Analytic Mathematics and Applications.

摘要/Abstract

摘要： In this paper, we study the pressure of C¹-smooth partially hyperbolic diffeomorphisms with sup-additive potentials. We give several definitions of the so called unstable (measure theoretic) pressure in terms of Bowen's picture and the capacity picture. We show that all such unstable metric pressures of a given ergodic measure equals the corresponding unstable measure theoretic entropy plus the Lyapunov exponent of the potentials with respect to the ergodic measure.

关键词: Partially hyperbolic systems, unstable measure theoretic pressure, sup-additive potentials

Abstract: In this paper, we study the pressure of C¹-smooth partially hyperbolic diffeomorphisms with sup-additive potentials. We give several definitions of the so called unstable (measure theoretic) pressure in terms of Bowen's picture and the capacity picture. We show that all such unstable metric pressures of a given ergodic measure equals the corresponding unstable measure theoretic entropy plus the Lyapunov exponent of the potentials with respect to the ergodic measure.

Key words: Partially hyperbolic systems, unstable measure theoretic pressure, sup-additive potentials

中图分类号:

37D35

张文达, 李智强. SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS[J]. 数学物理学报(英文版), 2022, 42(2): 575-587.

Wenda ZHANG, Zhiqiang LI. SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS[J]. Acta mathematica scientia,Series B, 2022, 42(2): 575-587.

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SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS

SUP-ADDITIVE METRIC PRESSURE OF DIFFEOMORPHISMS

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