Thermodynamic Formalism for Random Non-uniformly Expanding Maps

• DOI: 10.1007/s00220-021-04088-w
• Publication Date: 2021-04-19T15:04:38Z
• Authors: Manuel Stadlbauer; Shintaro Suzuki; Paulo Varandas
• Keywords: Formalism (music); Random compact set

58 pages, revised version<br/>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.<br/>