On the dynamical properties of a Fermi accelerator model

In this paper we use discrete dynamical systems formalism to carefully investigate the effect of a time-dependent perturbation on a classical mechanical model. We present a study of a one-dimensional Fermi accelerator model and its parametric dependence on the amplitude of the movement of the wall. We focus on the low-energy region, in which the system may present chaotic behavior illustrated by orbits with stochastic behavior and sensitive dependence on initial conditions. Through numerical analysis, this behavior is quantitatively characterized by a positive Lyapunov exponent and by the position of the boundary of the observed ergodic component. Our results will be analyzed by comparing this model to a simplified version and to the Standard Map. These results indicate that the dynamics of the model is, in a certain sense, very weakly dependent of the parameter.