Geodesic
Physical measures for infinite-modal maps
Vítor Araújo 1   ; Maria José Pacifico 2
1 Instituto 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
2 Instituto de Matemática Universidade Federal do Rio de Janeiro C. P. 68.530 21.945-970 Rio de Janeiro, R. J., Brazil
Fundamenta Mathematicae, Tome 203 (2009) no. 3, pp. 211-262 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm203-3-2
Keywords: analyze certain parametrized families one dimensional maps infinitely many critical points measure theoretical point view prove families have absolutely continuous invariant probability measures positive lebesgue measure subset parameters moreover density measure its entropy vary continuously parameter addition obtain exponential rate mixing these measures satisfy central limit theorem

Vítor Araújo  1   ; Maria José Pacifico  2

1 Instituto 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
2 Instituto de Matemática Universidade Federal do Rio de Janeiro C. P. 68.530 21.945-970 Rio de Janeiro, R. J., Brazil 
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Vítor Araújo; Maria José Pacifico. Physical measures for infinite-modal maps. Fundamenta Mathematicae, Tome 203 (2009) no. 3, pp. 211-262. doi: 10.4064/fm203-3-2

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