# Cohomology of fiber-bunched twisted cocycles over hyperbolic systems

## TL;DR

This paper proves that fiber-bunched twisted cocycles over hyperbolic systems with the same periodic data are cohomologous, extending classical results to a broader class of cocycles with automorphism twists.

## Contribution

It establishes a cohomology classification for fiber-bunched twisted cocycles valued in GL(d,R) over hyperbolic systems, based on periodic data equivalence.

## Key findings

- Twisted cocycles with fiber-bunching are cohomologous if they share the same periodic data.
- The result generalizes classical cohomology theorems to cocycles twisted by automorphisms.
- Provides a criterion for cohomology in the context of Lie group-valued cocycles.

## Abstract

A twisted cocycle taking values on a Lie Group $G$ is a cocycle that, in each step, is twisted by an automorphism of $G$. In the case when $G=GL(d,\mathbb{R})$, we prove that if two H\"older continuous twisted cocycles satisfying the so called fiber-bunching condition have the same periodic data then they are cohomologous.