Complete hyperbolicity in Hamiltonian systems with linear potential and elastic collisions (Q1573856)

The author studies completely hyperbolic systems and presents a class of systems with all Lyapunov exponents different from zero (completely hyperbolic), which are obtained by the restriction of the configuration space of a simple completely integrable system with linear potential and elastic collisions. As a result the following two questions arise: 1) How to extend the scheme to more general systems? 2) Are there any physically natural systems that fit into this limited scheme? The author does not know the answer to the first question. As for the second question, the author investigates the dynamics in 2-dimensional wedges and demonstrates, an interesting system in which there exists coexistence of hyperbolic components with a packet of invariant tori. The packet becomes thinner and thinner as the energy increases, until at the critical level only one invariant torus remains, dividing the energy shell into two components. For even bigger energies the two components coalesce.