Backward inducing and exponential decay of correlations for partially hyperbolic attractors

We study partially hyperbolic attractors ofC ² diffeomorphisms on a compact manifold. For a robust (non-empty interior) class of such diffeomorphisms, we construct Sinai-Ruelle-Bowen measures, for which we prove exponential decay of correlations and the central limit theorem, in the space of Hölder continuous functions. The techniques we develop (backward inducing, redundancy elimination algorithm) should be useful in the study of the stochastic properties of much more general non-uniformly hyperbolic systems.