Weak Gibbs Measures for Local Homeomorphisms

2025/10/23 by Ferreira, Giovane, Ramos, Vanessa
#37A05 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.20938

Abstract

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations principle. Furthermore, we extend these results to a class of attractors that are semiconjugate to local homeomorphisms from our original setting. Our approach is based on non-uniform conformal-like property and applies to a wide range of topological dynamical systems, including non-uniformly expanding maps, zooming local homeomorphisms, attractors arising from solenoid-like constructions and certain families of partially hyperbolic horseshoes.

Citations

• Thermodynamic formalism for expanding measures
• Weak Gibbs and Equilibrium Measures for Shift Spaces
• Equilibrium stability for non-uniformly hyperbolic systems
• The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows
• On the preservation of Gibbsianness under symbol amalgamation
• Non-uniform specification and large deviations for weak Gibbs measures
• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
• Projection of Markov measures may be Gibbsian

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• Attractor properties of non-reversible dynamics w.r.t invariant Gibbs measures on the lattice
• SRB measures for partially hyperbolic attractors of local diffeomorphisms