arXiv subjects

Vanessa Ramos

Publications and source records attributed to Vanessa Ramos.

5 recordsLinked to original sources

arXiv2025

Weak Gibbs Measures for Local Homeomorphisms

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.

math.DS↗

arXiv2021

Equilibrium states for non-uniformly hyperbolic systems: statistical properties and analyticity

We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials.

math.DS↗

arXiv2020

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

We consider a robust class of random non-uniformly expanding local homeomorphisms and Hölder continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and uniqueness of equilibrium states among non-uniformly expanding measures. Moreover, we show that these equilibrium states and the random topological pressure vary continuously in this setting.

math.DS↗

arXiv2017

Equilibrium stability for non-uniformly hyperbolic systems

We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the topological pressure is continuous as a function of the dynamics and the potential. We also prove the existence of finitely many ergodic equilibrium states for non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials. Finally we show that these equilibrium states vary continuously in the weak$^\ast$ topology within such systems.

math.DS↗

arXiv2016

On statistical properties for equilibrium states of partially hyperbolic horseshoes

We derive some statistical properties for equilibrium states of partially hyperbolic horseshoes. We define a projection map associated to the horseshoe and prove a spectral gap for its transfer operator acting on the space of Hölder continuous observables. From this we deduce an exponential decay of correlations and a central limit theorem. We finally extend these results to the horseshoe.

math.DS↗