CHAOTIC, REGULAR AND UNBOUNDED BEHAVIOR IN THE ELASTIC IMPACT OSCILLATOR

We study the elastic impact oscillator which is a periodically-forced mass on a spring impacting against a rigid wall. This gives rise to an area-preserving mapping that typically displays chaos at low energies and regular behaviour at high energies. The boundary between the two types of behaviour is complicated by the existence of discontinuities. The high energy behaviour is strongly influenced by resonances and th e existence of invariant curves that bound the energy gain of the mass has an interesting dependence upon the system parameters.