On the Lyapunov spectrum of relative transfer operators

TL;DR

This paper investigates the Lyapunov spectrum of relative Ruelle operators in skew product systems, demonstrating they can be approximated by positive matrices with dominated splittings, advancing understanding of their spectral properties.

Contribution

It introduces a method to approximate the Lyapunov spectrum of relative transfer operators using positive matrices with dominated splittings.

Findings

Lyapunov spectrum can be approximated in $C^0$-topology

Operators can be approximated by positive matrices

Dominated splitting is established for these approximations

Abstract

We analyze the Lyapunov spectrum of the relative Ruelle operator associated with a skew product whose base is an ergodic automorphism and whose fibers are full shifts. We prove that these operators can be approximated in the $C^0$-topology by positive matrices with an associated dominated splitting.