### Geometry of expanding absolutely continuous invariant
measures and the liftability problem

Jose Alves

Abstract:
We consider a broad class of maps f on compact manifolds
of arbitrary dimension possibly admitting critical points,
discontinuities and singularities. Under some mild nondegeneracy
assumptions we show that f admits an induced Gibbs-Markov map
with integrable inducing times if and only if it has an ergodic
invariant probability measure which is absolutely continuous with
respect to the Riemannian volume and has only positive Lyapunov exponents.