Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit

Abstract

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual ${\mathcal{C}}^0$ topology and $\varphi :M\to \mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$ of End($M$) such that, if $f\in \mathcal{A}$, there exists a $f$ invariant measure ${\mu }_{\max }$ supported on a periodic orbit that maximizes the integral of $\varphi$ among all $f$ invariant Borel probability measures.

arXiv commentTo appear in Discrete Contin. Dyn. Sys. - A

Cited by in corpus (2)

• Ergodic optimization in dynamical systems
• Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits