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 $\sup_{\mu \in M_{\tilde T}}\int f d\mu \leq \sup_{\mu \in M_{T}}\int f d\mu$.
@article{30819,
title = {A note on eventually periodic endomorphisms and their maximizing measures},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i3.30819},
language = {EN},
url = {http://dml.mathdoc.fr/item/30819}
}
Gonschorowski, Juliano. A note on eventually periodic endomorphisms and their maximizing measures. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i3.30819. http://gdmltest.u-ga.fr/item/30819/