Physical measures for infinite-modal maps
Volume 203 / 2009
Fundamenta Mathematicae 203 (2009), 211-262
MSC: Primary 37C40; Secondary 37D25, 37A25, 37A35.
DOI: 10.4064/fm203-3-2
Abstract
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.
