Hidden High Period Accelerator Modes in a Bouncer Model

Abstract

We characterized the influence of high period accelerator modes in the global dynamics of a non-dissipative Bouncer model. The dynamics of the system was investigated considering both complete and simplified approaches. Evaluating the average of the velocity over large ensembles of initial conditions for the complete mapping, we obtained particular ranges of the control parameter where high period accelerating structures are located. The position, influence and shape of the accelerator modes were obtained considering the symplectic mapping. Our results, lead us to infer that even for high period and less influent accelerator modes, the dynamics is globally affected for long time series, causing an anomalous diffusion, in compare with the regular Fermi acceleration.