Preprint A328/2004
Physical measures for infinite-modal maps

Maria José Pacífico | Araújo, Vítor

**Keywords: **
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.