Physical measures for infinite-modal maps

• Autorzy: Vítor Araújo , Maria José Pacifico
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37A25: Ergodicity, mixing, rates of mixing
• 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 203
• Numer: 3
• Strony: 211-262

Daty

wydano

2009

Twórcy

autor

Vítor Araújo

• Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21.945-970 Rio de Janeiro, R. J., Brazil
• Centro de Matemática, da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

autor

Maria José Pacifico

• Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21.945-970 Rio de Janeiro, R. J., Brazil

Identyfikatory

DOI

10.4064/fm203-3-2