Dynamics of a charged particle in a dissipative Fermi–Ulam model

• A Fermi–Ulam model with electric force and friction is regarded.
• Attractors and unbounded orbits coexist in the simplified model.
• Islands of regular motion and attractor coexist in the complete model.
• The coexistence occur for null electric force in the complete model.
• This coexistence may be observed in time dependent two-dimensional billiards.

The dynamics of a metallic particle confined between charged walls is studied. One wall is fixed and the other moves smoothly and periodically in time. Dissipation is considered by assuming a friction produced by the contact between the particle and a rough surface. We investigate the phase space of the simplified and complete versions of the model. Our results include (i) coexistence of islands of regular motion with an attractor located at the low energy portion of phase space in the complete model and; (ii) coexistence of attractors with trajectories that present unlimited energy growth in the simplified model.