题目: Equilibrium states of partially hyperbolic horseshoes: uniqueness and statistical properties
报告人：Jaqueline Siqueira, Puc-Rio, Brazil
摘要: We prove uniqueness of equilibrium states of partially hyperbolic horseshoes associated to Holder continuous potentials with small variation. (Joint work with Isabel Rios). In order to derive some statistical properties for the unique equilibrium state we define a projection map associated to the horseshoe and prove a spectral gap for its transfer operator acting on the space of Holder continuous observables. From this we deduce an exponential decay of correlations and a central limit theorem. Finally, we extend these results to the horseshoe. (Joint work with Vanessa Ramos.)
题目： Equilibrium stability for non-uniformly hyperbolic maps
报告人:Jaqueline Siqueira, Puc-Rio, Brazil
摘要: We consider a wide family of non-uniformly hyperbolic maps and hyperbolic potentials and prove that the equilibrium states persist under small perturbations. This phenomena we call equilibrium stability. In order to obtain this result we deduce that the topological pressure is continuous in the $C^1$ topology 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 H\"older continuous potentials. Finally we show that these equilibrium states vary continuously in the weak$^\ast$ topology within such systems. This is a joint work with José Alves and Vanessa Ramos.