Liv\v{s}ic theorems for Banach cocycles: existence and regularity
Dynamical Systems
2020-04-03 v1
Abstract
We prove a nonuniformly hyperbolic version Liv\v{s}ic theorem, with cocycles taking values in the group of invertible bounded linear operators on a Banach space. The result holds without the ergodicity assumption of the hyperbolic measure. Moreover, We also prove a -continuous solution of the cohomological equation is actually H\"older continuous for the uniform hyperbolic system.
Keywords
Cite
@article{arxiv.2004.00928,
title = {Liv\v{s}ic theorems for Banach cocycles: existence and regularity},
author = {Rui Zou and Yongluo Cao},
journal= {arXiv preprint arXiv:2004.00928},
year = {2020}
}