Absolutely continuous invariant measures for non-uniformly expanding skew-products
absolutely continuous invariant measures | weak expansion | critical points | slow recurrence to the critical set
We prove that for certain partially hyperbolic skew-products on the cylinder, non-uniform hyperbolicity along the leaves implies existence of absolutely continuous invariant probability measures. The main technical tool is an extension for sequences of maps of a result of de Melo and van Strien relating hyperbolicity to recurrence properties of orbits. As a consequence of our main result, we obtain extensions of Keller's theorem guaranteeing the existence of absolutely continuous invariant measures for non-uniformly hyperbolic one dimensional maps.