A note on eventually periodic endomorphisms and their maximizing measures

Abstract

Given an eventually periodic endomorphism $T$ defined on a compact metric space $K$ we constructed another endomorphism $\tilde T:K\rightarrow K$ that is $C^0$-close of $T$, has a nonperiodic orbit and such that $\sup_{\mu \in M_{\tilde T}}\int f d\mu \leq \sup_{\mu \in M_{T}}\int f d\mu$.