2008/03/18 by Paulo Varandas, Marcelo Viana, Varandas, Paulo +1 · 4 citations
Mathematics · Physics and Astronomy · #37D25 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.DS #msc:37D25 #msc:37D35
paper · pdf · doi:10.48550/arxiv.0803.2654
44 pages
arxiv created 2008/03/18 · openalex publication_date 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Holder continuous potentials with not very large oscillation. No Markov structure is assumed. If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property. Under mild additional assumptions we also prove that the equilibrium states vary continuously with the dynamics and the potentials (statistical stability) and are also stable under stochastic perturbations of the transformation.