H\"{o}lder continuity of Oseledets subspaces for linear cocycles on Banach spaces

TL;DR

This paper proves the H"{o}lder continuity of Oseledets subspaces for both invertible and non-invertible operator cocycles on Banach spaces, extending previous results and covering a broader class of systems.

Contribution

It extends the H"{o}lder continuity results of Oseledets subspaces to non-invertible cocycles on Banach spaces, broadening the scope of prior work.

Findings

H"{o}lder continuity of Oseledets subspaces established for invertible cocycles.

Extension of H"{o}lder continuity results to non-invertible cocycles.

Results hold over a large measure set in the base space.

Abstract

Let $f:X\to X$ be an invertible Lipschitz transformation on a compact metric space $X$. Given a H\"{o}lder continuous invertible operator cocycles on a Banach space and an $f$-invariant ergodic measure, this paper establishes the H\"{o}lder continuity of Oseledets subspaces over a compact set of arbitrarily large measure. This extends a result in \cite{Simion16} for invertible operator cocycles on a Banach space. Finally, this paper proves the H\"{o}lder continuity in the non-invertible case.