Geodesic
On maximizing measures of homeomorphisms on compact manifolds
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
Fundamenta Mathematicae, Tome 200 (2008) no. 2, pp. 145-159 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm200-2-3
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

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 
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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

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