On conformal measures and harmonic functions for group extensions

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.

To appear in Proceedings of "New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo"

Cited by in corpus (2)

• The Martin boundary of an extension by a hyperbolic group
• Discrete group extensions of countable Markov shifts and pressure gap