Statistical properties of hyperbolic systems with tangential singularities

We consider piecewise smooth, uniformly hyperbolic systems on a Riemannian manifold, where we allow the angle between the unstable direction and the singularity manifolds to vanish. Under natural assumptions we prove that such systems exhibit exponential decay of correlations and satisfy a central limit theorem with respect to a mixing Sinai-Ruelle-Bowen-measure. These results have been shown previously for systems in which the angle between the singularity manifold and the unstable direction is uniformly bounded away from zero.