TIME-DEPENDENT BILLIARDS

This is an attempt to study mathematically billiards with moving bound aries. We assume that the boundary remains closed, regular and strictl y convex, deforming periodically in time, in the normal direction. We describe the associated billiard diffeomorphism and the corresponding invariant measure. We discuss the stability of 2-periodic orbits and i nvestigate the boundedness of the velocity in some precise examples. F inally, we present the Hamiltonian formalism and the symplectic struct ure, considering that a moving billiard is a billiard with rigid bound ary on an augmented configuration space, with a singular metric.