Semigroup actions of expanding maps

Abstract

We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the thermodynamic formalism of the associated skew-product. In particular, we clarify the connection between the topological entropy of the semigroup action and the growth rate of the periodic points, establish the main properties of the dynamical zeta function of the semigroup action and prove the existence of stationary probability measures.

A few typos were corrected, Sections 8 and 9 were improved and a variational relation for the relative entropy has been included in Section 8

References in corpus (2)

• Specification properties and thermodynamical properties of semigroup actions
• Coupling methods for random topological Markov chains

Cited by in corpus (3)

• Quenched and annealed equilibrium states for random Ruelle expanding maps and applications
• The upper capacity topological entropy of free semigroup actions for certain non-compact sets,$II$
• Entropy points and applications for free semigroup actions