Inelastic gravitational billiards

Dynamical aspects of a bouncing ball in a nonhomogeneous field

We study some dynamical properties of a charged particle that moves in a nonhomogeneous electric field and collides against an oscillating platform. Depending on the values of parameters, the system presents (i) predominantly regular dynamics or (ii) structures of chaotic behavior in phase space conditioned to the initial conditions. The localization of the fixed points and their stability are carefully discussed. Average properties of the chaotic sea are investigated under a scaling approach. We show that the system belongs to the same universality class as the Fermi-Ulam model.

Billiard with a handle

We consider an open billiard with two holes, connected by a handle. The central billiard is chosen so that its closed form's islands of stability occupy a significant part of the phase space. Holes destroy these islands, which leads to almost all trajectories of the system being interleaved. We also study the unbalanced flow of billiard particles through the handle, which appears only after a small border site of nonspecular reflection is added to the system. With this site our system is rather a ratchet of a different type, since the site does not produce an explicitly acting force or violate the reversibility of trajectories.