| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Bristol, Sch Math, Bristol, Avon - England
[2] UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil
[3] Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo - Brazil
[4] Abdus Salaam Int Ctr Theoret Phys, Abdus Salam, I-34151 Trieste - Italy
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 22, n. 1-3, p. 731-746, MAY 2015. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regimes is made. The linear stability of fixed points is studied, yielding exact analytical expressions for parameter values at which a period-doubling bifurcation occurs. The dynamics is apparently ergodic at certain energies in all three models, in contrast to the regularity of the circular and elliptic billiard dynamics in the field-free case. This finding is confirmed using a sensitive test involving Lyapunov weighted dynamics. In the last part of the paper a time dependence is introduced in the billiard boundary, where it is shown that for the circular billiard the average velocity saturates for zero gravitational force but in the presence of gravitational it increases with a very slow growth rate, which may be explained using Arnold diffusion. For the oval billiard, where chaos is present in the static case, the particle has an unlimited velocity growth with an exponent of approximately 1/6. (C) 2014 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 12/18962-0 - Transport, escape of particles and dynamical properties of some non-linear mappings |
| Grantee: | Diogo Ricardo da Costa |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 13/22764-2 - Dynamical and transport properties in conservative and dissipative dynamical systems |
| Grantee: | Diogo Ricardo da Costa |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Regular Research Grants |