Livšic theorem for matrix cocycles over nonuniformly hyperbolic systems-Reference-Cited by-同舟云学术

Livšic theorem for matrix cocycles over nonuniformly hyperbolic systems

Published:2019-03-27 Issue:02 Volume:19 Page:1950010
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Zou Rui¹,Cao Yongluo¹²

Affiliation:

1. School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China

2. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200062, P. R. China

Abstract

We prove a nonuniformly hyperbolic version of the Livšic-type theorem, with cocycles taking values in [Formula: see text]. To be more precise, let [Formula: see text] Diff[Formula: see text] preserving an ergodic hyperbolic measure [Formula: see text], and [Formula: see text] be Hölder continuous satisfying [Formula: see text] for each periodic point [Formula: see text], then there exists a measurable function [Formula: see text] satisfying [Formula: see text] for [Formula: see text]-almost every [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493719500102

Reference14 articles.

1. Nonuniform Hyperbolicity

2. Exponential closing property and approximation of Lyapunov exponents of linear cocycles

3. On Livšic’s theorem, superrigidity, and Anosov actions of semisimple Lie groups

4. Livšic theorem for banach rings

5. Livšic Theorem for matrix cocycles

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4. A Livšic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems;Journal of Dynamics and Differential Equations;2018-07-24