Convex and functional analysis approachesto thermodynamic formalism

Paulo Varandas, Universidade de Aveiro

Abstract:

The thermodynamic formalism for transitiveuniformly hyperbolic dynamics is nowadays well understood and, among other aspects, it is worth mentioning that regular potentials (meaning Holder continuous) are so that the pressure function is differentiable and admit unique equilibrium states. The situation changes drastically for dynamical systems beyond the framework of uniform hyperbolicity and in non-dynamical contexts as the framework of group actions and foliations. In this talk I will illustrate the use of convex and functional analysis in the study of phase transition of Manneville-Pomeau maps and thermodynamic formalism of both group actions and foliations.