Abstract. Some dynamical properties of a bouncing ball model under the presence of an external force modelled by two nonlinear terms are studied. The description of the model is made by the use of a two-dimensional nonlinear measure-preserving map on the variable's velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

PACS numbers: 05.45.−a, 05.45.Ac, 05.45.Pq

Print publication: Issue 1 (11 January 2008)
Received 15 August 2007, in final form 31 October 2007
Published 12 December 2007