SRB measures for non-hyperbolic systems with multidimensional expansion

We construct ergodic absolutely continuous invariant probability measures for an open class of non-hyperbolic surface maps introduced by Viana (1997), who showed that they exhibit two positive Lyapunov exponents at almost every point. Our approach involves an inducing procedure, based on the notion of hyperbolic time that we introduce here, and contains a theorem of existence of absolutely continuous invariant measures for multidimensional piecewise expanding maps with countably many domains of smoothness. (C) 2000 Editions scientifiques et medicales Elsevier SAS.