On conformal measures and harmonic functions for group extensions

TL;DR

This paper establishes a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains, introducing a method to construct conformal measures and harmonic functions with potential applications in dynamical systems.

Contribution

It provides a new Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains using $\sigma$-finite conformal measures, advancing the understanding of harmonic functions.

Findings

Constructed $\sigma$-finite conformal measures for group extensions.

Proved a Perron-Frobenius-Ruelle theorem in this context.

Applied results to the construction of harmonic functions.

Abstract

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.