On maximizing measures of homeomorphisms on compact manifolds

Tom 200 / 2008

Fábio Armando Tal, Salvador Addas-Zanata Fundamenta Mathematicae 200 (2008), 145-159 MSC: 37A05, 37B99, 46A55. DOI: 10.4064/fm200-2-3

Streszczenie

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.

Autorzy

  • Fábio Armando TalInstituto de Matemática e Estatística
    Universidade de São Paulo
    Rua do Matão 1010, Cidade Universitária
    05508-090 São Paulo, SP, Brazil
    e-mail
  • Salvador Addas-ZanataInstituto de Matemática e Estatística
    Universidade de São Paulo
    Rua do Matão 1010, Cidade Universitária
    05508-090 São Paulo, SP, Brazil
    e-mail

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