Rigidity of Fiber Bunched Cocycles

TL;DR

This paper establishes a rigidity result for fiber bunched matrix cocycles over hyperbolic systems, showing cohomology equivalence is characterized by conjugated periodic data.

Contribution

It proves a new rigidity theorem linking cohomology of fiber bunched cocycles to their periodic data conjugacy.

Findings

Cocycles are cohomologous iff their periodic data are conjugate.

The result applies to matrix-valued Hölder cocycles over hyperbolic homeomorphisms.

Provides a criterion for cohomology based on periodic data.

Abstract

We prove a rigidity theorem for fiber bunched matrix-valued Holder cocycles over hyperbolic homeomorphisms. More precisely, we show that two such cocycles are cohomologous if and only if they have conjugated periodic data.