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Physical measures for infinite-modal maps

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Araújo V., Pacifico M.

Fundamenta Mathematicae

2009

tom 203

nr 3

211-262

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.

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1 Fundamenta Mathematicae

1 Araújo V.

1 Pacifico M.

1 2009

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Physical measures for infinite-modal maps