| Full text | |
| Author(s): |
da Costa, Diogo Ricardo
[1, 2, 3]
;
Dettmann, Carl P.
[2]
;
de Oliveira, Juliano A.
[4]
;
Leonel, Edson D.
[3]
Total Authors: 4
|
| Affiliation: | [1] Univ Sao Paulo, Inst Fis, BR-05314970 Sao Paulo - Brazil
[2] Univ Bristol, Sch Math, Bristol, Avon - England
[3] UNESP Univ Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP - Brazil
[4] UNESP Univ Estadual Paulista, Sao Joao Da Boa Vista, SP - Brazil
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | Chaos; v. 25, n. 3 MAR 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around -3. The results here can be generalized to other kinds of external boundaries. (C) 2015 AIP Publishing LLC. (AU) | |
| 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 |
| FAPESP's process: | 14/18672-8 - Effects of dissipation, transient and dynamical properties in discrete mappings |
| Grantee: | Juliano Antonio de Oliveira |
| Support Opportunities: | Regular Research Grants |
| 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 |