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arXiv · 2302.02911

Cocycles measurably conjugate to unipotent over hyperbolic systems

Jonathan DeWitt
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Abstract

We show that if a H\"{o}lder continuous linear cocycle over a hyperbolic system is measurably conjugate to a cocycle taking values in a unipotent group, then the cocycle is H\"older continuously conjugate to a cocycle taking values in a unipotent group. More generally, we introduce some natural classes of matrices contained in ${\rm GL}(d,\mathbb{R})$, which we call Zimmer blocks. Examples of Zimmer blocks are unipotent and compact subgroups. We show that the same conclusion holds for Zimmer blocks.

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Jonathan DeWitt. 2023-02-06. Cocycles measurably conjugate to unipotent over hyperbolic systems. https://arxiv.org/abs/2302.02911

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