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arXiv · 2204.10117

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

Chiyi Luo·Yun Zhao
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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.

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Chiyi Luo, Yun Zhao. 2022-04-21. H\"{o}lder continuity of Oseledets subspaces for linear cocycles on Banach spaces. https://doi.org/10.1088/1402-4896%2Faca3d9

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