Physical measures for infinite-modal maps

Details Physical measures for infinite-modal maps Physical measures for infinite-modal maps

2004-11-22

arxiv.org/abs/math/0411493v5

Fundamenta Mathematicae, v. 203, p. 211-262, 2009

Mathematics

Dynamical Systems

41 pages, 3 figures, some proofs completely rewritten. Keywords: SRB measures, absolutely continuous invariant measures, infin

Scientific paper

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 densities of these measures and their entropy vary continuously with the parameter. In addition we obtain exponential rate of mixing for these measures and also that they satisfy the Central Limit Theorem.

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