Semigroup actions of expanding maps
Dynamical Systems
2017-02-01 v2
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.
Cite
@article{arxiv.1601.04275,
title = {Semigroup actions of expanding maps},
author = {Maria Carvalho and Fagner B. Rodrigues and Paulo Varandas},
journal= {arXiv preprint arXiv:1601.04275},
year = {2017}
}
Comments
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