Huyi Hu (University of Southern California)

Absolutely continuous invariant measures for non-uniformly expanding maps.

Abstract. This is a joint work with Sandro Vaienti. We consider some multidimensional piecewise smooth expanding maps with an indifferent fixed point that may not have Markov partition. We show that such systems admit absolutely continuous invariant measures $\mu$ that has at most finitely many ergodic components, which are either finite or sigma-finite. Also, examples show that $\mu$ may has both finite and sigma-finite ergodic components simultaneously, and both contain the indifferent fixed point in their supports.