Cohomology of Lipschitz-valued cocycles
Dynamical Systems
2025-08-21 v1
Abstract
We consider the set of H\"older continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over periodic points of the base are cohomologous, with the conjugacy being H\"older continuous. Moreover, we prove that, under an additional condition, the existence of a measurable conjugacy implies the existence of a H\"older continuous conjugacy between the cocycles.
Keywords
Cite
@article{arxiv.2508.14446,
title = {Cohomology of Lipschitz-valued cocycles},
author = {Marisa Cantarino and Catalina Freijo},
journal= {arXiv preprint arXiv:2508.14446},
year = {2025}
}