Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems

TL;DR

This paper proves that for a broad class of linear cocycles over non-uniformly hyperbolic systems, the Lyapunov spectrum is generically simple, confirming a conjecture by Viana.

Contribution

It establishes the simplicity of Lyapunov spectra for fiber-bunched, H"older continuous cocycles over non-uniformly hyperbolic systems, confirming Viana's conjecture.

Findings

Lyapunov spectrum is simple for generic fiber-bunched cocycles

Confirms Viana's conjecture in this context

Applicable to systems with u-Gibbs measures

Abstract

We prove that generic fiber-bunched and H\"older continuous linear cocycles over a non-uniformly hyperbolic system endowed with a u-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched cocycles.