Edson D Leonel and Mario Roberto Silva 2008 J. Phys. A: Math. Theor. 41 015104 doi:10.1088/1751-8113/41/1/015104
A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration
Edson D Leonel and Mario Roberto Silva
Show affiliationsSome 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
- MSC
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37D45 Strange attractors, chaotic dynamics
70K55 Transition to stochasticity (chaotic behavior) (See also 37D45)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
70Fxx Dynamics of a system of particles, including celestial mechanics
- Subjects
- Dates
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Issue 1 (11 January 2008)
Received 15 August 2007, in final form 31 October 2007
Published 12 December 2007
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A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration
Edson D Leonel and Mario Roberto Silva 2008 J. Phys. A: Math. Theor. 41 015104
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