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<p>We show that if a Hölder continuous linear cocycle over a hyperbolic system is measurably conjugate to a cocycle taking values in a unipotent group, then the cocycle is Hölder continuously conjugate to a cocycle taking values in a unipotent group. More generally, we introduce some natural classes of matrices contained in GL(<i>d</i>, 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.</p>

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Cocycles measurably conjugate to unipotent over hyperbolic systems

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Jonathan DeWitt

摘要

We show that if a Hölder continuous linear cocycle over a hyperbolic system is measurably conjugate to a cocycle taking values in a unipotent group, then the cocycle is Hölder continuously conjugate to a cocycle taking values in a unipotent group. More generally, we introduce some natural classes of matrices contained in GL(d, 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.