On maximizing measures of homeomorphisms on compact manifolds
Volume 200 / 2008
Fundamenta Mathematicae 200 (2008), 145-159
MSC: 37A05, 37B99, 46A55.
DOI: 10.4064/fm200-2-3
Abstract
We prove that given a compact $n$-dimensional connected Riemannian manifold $X$ and a continuous function $g:X\rightarrow \mathbb R$, there exists a dense subset of the space of homeomorphisms of $X$ such that for all $T$ in this subset, the integral $\int_X g\, d\mu$, considered as a function on the space of all $T$-invariant Borel probability measures $\mu$, attains its maximum on a measure supported on a periodic orbit.
