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.