Statistical properties of piecewise smooth hyperbolic systems in high dimensions

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