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.

Anexos:

• novoinfinite.pdf