PSEUDO-BILLIARDS

A new class of Hamiltonian dynamical systems with two degrees of freed om and kinetic energy of the form T = c(1)\p(1)\ + c(2)\p(2)\ (called ''pseudo-billiards'') is studied. For any kind of interaction, the can onical equations can always be integrated on sequential time intervals ; i.e. in principle all the trajectories can be found explicitly. Depe nding on the potential, a dynamical system of this class can either be completely integrable or behave just as a usual non-integrable Hamilt onian system with two degrees of freedom: in its phase space there exi st invariant tori, stochastic layers, domains of global chaos, etc. Ps eudo-billiard models of both the types are considered. If a potential of a pseudo-billiard system has critical points (equilibria), then tra jectories close to these points (''loops'') can exist; they can be tre ated as images of self-localized objects with finite duration. Such a model (with quartic potential) is also studied.