Thermodynamic formalism and dynamical zeta functions

Title: Thermodynamic formalism and dynamical zeta functions for transfer operators of piece-wise expanding maps in finite dimension

Abstract: In the last years, an extremely powerful method has been developed to study the statistical properties of a dynamical system: the functional approach. It consists in the study of the spectral properties of the transfer operator (dual of the composition operator) on suitable Banach spaces.

In this talk I will show how to obtain good spectral properties (in terms of thermodynamic quantities) of weighted transfer operators associated to a piece-wise expanding map on a compact manifold with finite dimension. I will also show how to use the results to get information on the dynamical zeta function associated to the systems.
This is a joint work in progress with Viviane Baladi.