LETTER TO THE EDITOR A crisis in the dissipative Fermi accelerator model

The dynamics of the full, dissipative, Fermi accelerator model is shown to exhibit crisis events as the damping coefficient is varied. The investigation, based on analysis of a two-dimensional nonlinear map, has also led to a numerical determination of the basin of attraction for its chaotic attractor. PACS numbers: 05.45.−a, 45.50.Dd A major challenge in the investigation of nonlinear systems is that of explaining/predicting the often unexpected phenomena that they exhibit. A closely related goal is to characterize their dynamical properties. Chaotic behaviour appears quite frequently in such systems, both in the presence and the absence of dissipation [1–3]. For the dissipative case, the area-contracting property leads to time evolution of initial conditions towards a range of different asymptotic behaviours, e.g. fixed points, limit cycles (sometimes of high order) as well as chaotic attractors. There also exist systems with more than one chaotic attractor [4] where interest frequently centres on determination of the basins of attraction for each chaotic attractor, whose boundaries can be either continuous or fractal. Particular cases can also b