Chaotic dynamics and orbit stability in the parabolic oval billiard

Scientific paper - Original scientific paper

• Author: Vjera Lopac
• Author: Ivana Mrkonjić
• Author: Danko Radić
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

Chaotic properties of the one-parameter family of oval billiards with parabolic boundaries are investigated. Classical dynamics of such billiard is mixed and depends sensitively on the value of the shape parameter. Deviation matrices of some low period orbits are analyzed. Special attention is paid to the stability of orbits bouncing at the singular joining points of the parabolic arcs, where the boundary curvature is discontinuous. The existence of such orbits is connected with the segmentation of the phase space into two or more chaotic components. The obtained results are illustrated by numerical calculations of the Poincaré sections and compared with the properties of the elliptical stadium billiards.

• Keywords (english): chaotic dynamics; orbit stability; billiard
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review E
• Numbering: vol. 66, no. 3, 036202
• p-ISSN: 1539-3755
• DOI: https://doi.org/10.1103/PhysRevE.66.036202
• URN:NBN: urn:nbn:hr:217:005059
• Publication: 2002
• Document URL: http://link.aps.org/doi/10.1103/PhysRevE.66.036202
• Type of resource: Text
• Access conditions: Open access
• Public note: Copyright (2002) by the American Physical Society.
• Created on: 2019-10-13 12:26:53