Physical measures for infinite-modal maps

Tom 203 / 2009

Vítor Araújo, Maria José Pacifico Fundamenta Mathematicae 203 (2009), 211-262 MSC: Primary 37C40; Secondary 37D25, 37A25, 37A35. DOI: 10.4064/fm203-3-2

Streszczenie

We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the Central Limit Theorem.

Autorzy

  • Vítor AraújoInstituto de Matemática
    Universidade Federal do Rio de Janeiro
    C. P. 68.530
    21.945-970 Rio de Janeiro, R. J., Brazil
    and
    Centro de Matemática
    da Universidade do Porto
    Rua do Campo Alegre 687
    4169-007 Porto, Portugal
    e-mail
  • Maria José PacificoInstituto de Matemática
    Universidade Federal do Rio de Janeiro
    C. P. 68.530
    21.945-970 Rio de Janeiro, R. J., Brazil
    e-mail

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