On the Lyapunov spectrum of relative transfer operators

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.

The article now contains a section on decay of correlations of relative transfer operators

References in corpus (3)

• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations
• Coherent structures and isolated spectrum for Perron-Frobenius cocycles
• On random topological Markov chains with big images and preimages

Cited by in corpus (6)

• Continuity of Lyapunov exponents is equivalent to continuity of Oseledets subspaces
• Quenched and annealed equilibrium states for random Ruelle expanding maps and applications
• Entropy, pressure, ground states and calibrated sub-actions for linear dynamics
• Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism
• On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients
• Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples