Equilibrium States for Random Non-uniformly Expanding Maps

Abstract

We show that, for a robust ($C^2$-open) class of random non-uniformly expanding maps, there exists equilibrium states for a large class of potentials.In particular, these sytems have measures of maximal entropy. These results also give a partial answer to a question posed by Liu-Zhao. The proof of the main result uses an extension of techniques in recent works by Alves-Araújo, Alves-Bonatti-Viana and Oliveira.

References in corpus (1)

• Random perturbations of non-uniformly expanding maps

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• Maximal entropy measures for Viana maps
• Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems
• Uniform hyperbolicity for random maps with positive Lyapunov exponents
• Expanding measure has nonuniform specification property on random dynamical system
• Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures