Preprint D14/2005
Physical measures for infinite-modal maps
Maria Jose Pacifico | Araujo, Vitor
Keywords: {SRB measures | absolutely continuous invariant measures | infinite-modal maps | statistical stability | exponential decay of correlations | central limit theorem | continuous variation of entropy
We analyse 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.