标题： Lipschitz值上循环的上同调 显示英文标题

标题： Cohomology of Lipschitz-valued cocycles

摘要： 我们考虑在紧致度量拓扑群G上的Lipschitz同胚群Lip(G)上作用的有限移位下的Hölder连续上循环的集合。 我们证明，两个在基空间周期点上相同的支配上循环是共轭的，共轭是Hölder连续的。 此外，我们在一个额外条件下证明，可测共轭的存在性意味着上循环之间存在Hölder连续的共轭。 显示英文摘要

摘要： 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.