COMPLETE HYPERBOLICITY IN HAMILTONIAN SYSTEMS WITH LINEAR POTENTIAL AND ELASTIC COLLISIONS

We present a class of systems with all Lyapunov exponents different from ^ero (completely hyperbolic). They are obtained by the restriction of the configuration space of a simple completely integrable system with linear potential and elastic collisions. We show that special geometry of the configuration space is necessary. We survey concrete realizations of this scheme discussed previously in [16j and elsewhere.