STATIC AND TIME-DEPENDENT PERTURBATIONS OF THE CLASSICAL ELLIPTIC BILLIARD

The elliptical billiard problem defines a two-dimensional integrable d iscrete dynamical system. Integrability not being a robust property, w e study some static and rime-dependent perturbations of this problem. For the static case, we observe the transition from integrability to c haos, on some perturbations of the ellipse. Then we study time-depende nt perturbations, supposing that the boundary deforms periodically wit h the time, remaining always an ellipse. We investigate numerically th e now four-dimensional phase space, looking mainly al the question of whether or not the velocity of a given trajectory may increase indefin itely.