Uniqueness and Stability of Equilibrium States for Random Non-uniformly\n Expanding Maps

2020/07/21 by Rafael Bilbao, Bilbao, Rafael, Vanessa Ramos +1
Mathematics · #37D25 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2007.11076

openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a robust class of random non-uniformly expanding local\nhomeomorphisms and H "older continuous potentials with small variation. For\neach element of this class we develop the Thermodynamical Formalism and prove\nthe existence and uniqueness of equilibrium states among non-uniformly\nexpanding measures. Moreover, we show that these equilibrium states and the\nrandom topological pressure vary continuously in this setting.\n

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