Statistical properties of piecewise smooth hyperbolic systems in high dimensions

We study smooth hyperbolic systems with singularities and their SRBmeasures. Here we assume that the singularities are submanifolds, the hyperbolicityis uniform aside from the singularities, and one-sided derivatives exist on the singularities. We prove that the ergodic SRB measures exist, are finitely many, andmixing SRB measures enjoy exponential decay of correlations and a central limittheorem. These properties have been proved previously only for two-dimensionalsystems.