Bifurcations of Snap-back Repellers with application to Border-Collision Bifurcations

The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in non-invertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations