We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g: X → ℝ, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral , considered as a function on the space of all T-invariant Borel probability measures μ, attains its maximum on a measure supported on a periodic orbit.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-2-3,
author = {F\'abio Armando Tal and Salvador Addas-Zanata},
title = {On maximizing measures of homeomorphisms on compact manifolds},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {145-159},
zbl = {1153.37305},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-2-3}
}
Fábio Armando Tal; Salvador Addas-Zanata. On maximizing measures of homeomorphisms on compact manifolds. Fundamenta Mathematicae, Tome 201 (2008) pp. 145-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-2-3/