Smale Horseshoe in a Piecewise Smooth Map

Abstract

We investigate the chaotic dynamics of a two-dimensional piecewise smooth map. The map represents the normal form of a discrete time representation of impact oscillators near grazing states. It is proved that, in certain region of the parameter space, the nonwandering set of the map is contained in a bounded region and that, restricted to the nonwandering set, the map is topologically conjugate to the two-sided shift map on two symbols.