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arXiv · 2004.00928

Liv\v{s}ic theorems for Banach cocycles: existence and regularity

Rui Zou·Yongluo Cao
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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 $\mu$-continuous solution of the cohomological equation is actually H\"older continuous for the uniform hyperbolic system.

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Rui Zou, Yongluo Cao. 2020-04-02. Liv\v{s}ic theorems for Banach cocycles: existence and regularity. https://arxiv.org/abs/2004.00928

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