Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems

Xinsheng Wang; Weisheng Wu; Yujun Zhu

doi:10.3934/dcds.2020004

Article Contents

2020, Volume 40, Issue 1: 81-105. Doi: 10.3934/dcds.2020004

This issue Previous Article Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line Next Article Regularity of extremal solutions of nonlocal elliptic systems

Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems

1.
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
2.
Department of Applied Mathematics, College of Science, China Agricultural University, Beijing 100083, China
3.
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

^* Corresponding author: Weisheng Wu
^* Corresponding author: Weisheng Wu

Received: October 2018

Revised: June 2019

Published online: January 2020

X. Wang and Y. Zhu are supported by NSFC (Nos: 11771118, 11801336), W. Wu is supported by NSFC (No: 11701559). The first author is also supported by the Innovation Fund Designated for Graduate Students of Hebei Province (No: CXZZBS2018101) and China Scholarship Council (CSC).

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Abstract

Let $ \mathcal{F} $ be a random partially hyperbolic dynamical system generated by random compositions of a set of $ C^2 $-diffeomorphisms. For the unstable foliation, the corresponding local unstable measure-theoretic entropy, local unstable topological entropy and local unstable pressure via the dynamics of $ \mathcal{F} $ along the unstable foliation are introduced and investigated. And variational principles for local unstable entropy and local unstable pressure are obtained respectively.

Keywords:

Random dynamical system,
local unstable measure-theoretic entropy,
local unstable topological entropy,
local unstable pressure,
variational principle.

Mathematics Subject Classification: Primary: 37D30, 37D35; Secondary: 37H99.

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