DSNT Seminar: Spectral properties of semigroups of expanding maps

Abstract: The dynamics of finitely generated semigroup actions has attracted the attention of many researchers, with the aim  of establishing variational principles and studying their topological, geometrical and ergodic theory aspects. Part of these goals have been attained whenever the generators satisfy some hyperbolicity conditions.
In this talk I will describe some spectral properties of semigroups of expanding maps,  show that there exists a limiting behaviour for the corresponding transfer operators, and that these semigroup actions admit equilibrium states with exponential decay of correlations. This is a joint work with M. Stadlbauer and X. Zhang.

This is a seminar in our seminar series on Dynamical Systems and Number Theory (DSNT).