Thermodynamic formalism for random non-uniformly expanding maps

Abstract

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered $C^1$-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.

arXiv comment58 pages, revised version

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Cited by in corpus (6)

• Thermodynamic Formalism for Random Weighted Covering Systems
• Equilibrium states for non-transitive random open and closed dynamical systems
• Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system
• Equilibrium States for Non-Uniformly Expanding Skew Products
• Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps
• Expanding measure has nonuniform specification property on random dynamical system