Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
By P. Varandas, Marcelo Viana. 2008
90 citations recorded by the source corpus.
Abstract We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact metric spaces 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.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/abf066f707adce3f6ed2a84f993c0ef31589e462
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Expanding Measures (2008, background): “Future applications Recently there was an increasing development of the study of the thermodynamic formalism beyond the uniformly hyperbolic context (including countable Markov shift) by several authors (this list is certainly not complete): Araujo [7], Arbieto, Matheus, Oliveira, Varandas, Viana [8”