Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit
Tatiane C. Batista Juliano S. Gonschorowski Fábio A. Tal
Discrete & Continuous Dynamical Systems - A 2015, 35(8): 3315-3326 doi: 10.3934/dcds.2015.35.3315
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 $\phi:M\to\mathbb{R}$ continuous. We prove, extending the main result of [2], 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 $\phi$ among all $f$ invariant Borel probability measures.
keywords: Maximizing measures periodic orbits.

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