English

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 μ\mu-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}
}