Continuity of Lyapunov exponents for non-uniformly fiber-bunched cocycles

TL;DR

This paper establishes conditions under which Lyapunov exponents vary continuously for certain non-uniform cocycles, extending previous results and addressing a conjecture in the field.

Contribution

It extends the continuity results of Lyapunov exponents to non-uniform fiber-bunched cocycles, advancing understanding in dynamical systems theory.

Findings

Provided new conditions for Lyapunov exponent continuity

Extended previous results to non-uniform settings

Addressed a conjecture of Marcelo Viana

Abstract

We provide conditions which imply the continuity of the Lyapunov exponents for non-uniformly fiber-bunched cocycles in $SL(2,\mathbb{R})$. The main theorem is an extension of the result of Backes, Brown and Butler and gives a partial answer to a conjecture of Marcelo Viana.