Sinai-Ruelle-Bowen measure for normal form map of grazing bifurcations of impact oscillators

Grazing bifurcations are typical non-smooth bifurcations that occur in impact oscillators. They are described by a discrete map with square-root singularities. In this paper we study the structure of a strange attractor which is the closure of the unstable manifold at hyperbolic fixed point of the normal form map for grazing bifurcations of one-degree-of-freedom impact oscillators from the ergodic theoretic point of view. We prove that for some set of values of the parameters this map has an Sinai-Ruelle-Bowen measure which is supported on the strange attractor and is ergodic.