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

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}$$continuous\mathrm{.}Weprovethatthereexistsadensesubsetof$$\mathcal{A}$$ofEnd($M$)suchthat,if$f\in$\mathcal{A}$$,thereexistsa$f$invariantmeasure$\mu_{\max}$ supported on a periodic orbit that maximizes the integral of $\varphi$ among all $f$ invariant Borel probability measures.