Physical measures for infinite-modal maps
Maria José Pacífico | Araújo, Vítor
SRB measures | absolutely continuous invariant measures | infinite-modal maps | statistical stability | sub-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 sub-exponential rate of mixing for these measures and also that they satisfy the Central Limit Theorem.