Maria Carvalho, Fagner B. Rodrigues, Paulo Varandas
Published 2016-12-21Version 1
We consider finitely generated free semigroup actions on a compact metric space and obtain quantitative information on Poincar\'e recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action. Besides, we relate the recurrence to balls with the rates of expansion of the semigroup's generators and the topological entropy of the semigroup action. Finally, we establish a partial variational principle and prove an ergodic optimization for this kind of dynamical action.
Every compact metric space that supports a positively expansive homeomorphism is finite
Topologically stable and $β$-persistent points of group actions
On supports of expansive measures
![QR code for arXiv:1612.07082 [math.DS]](http://oss.arxitics.com/images/favicon.svg)