SRB measures for non-hyperbolic systems with multidimensional expansion

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