Entropy points and applications for free semigroup actions

The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a free semigroup action, show that this set carries the full entropy of the system (which, with respect to the chaocity of the system, gives a fundamental relevance to such set). We prove that the topological entropy of a free semigroup action focuses on a countable set of points. Our results are inspired by the ones presented in [1]