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.
Keywords:
prove given compact n dimensional connected riemannian manifold continuous function rightarrow mathbb there exists dense subset space homeomorphisms subset integral int considered function space t invariant borel probability measures attains its maximum measure supported periodic orbit
Affiliations des auteurs :
Fábio Armando Tal
1
;
Salvador Addas-Zanata
1
1
Instituto de Matemática e Estatística Universidade de São Paulo Rua do Matão 1010, Cidade Universitária 05508-090 São Paulo, SP, Brazil
@article{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},
pages = {145--159},
year = {2008},
volume = {200},
number = {2},
doi = {10.4064/fm200-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm200-2-3/}
}
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AU - Fábio Armando Tal
AU - Salvador Addas-Zanata
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Fábio Armando Tal; Salvador Addas-Zanata. On maximizing measures of homeomorphisms on compact manifolds. Fundamenta Mathematicae, Tome 200 (2008) no. 2, pp. 145-159. doi: 10.4064/fm200-2-3
