On Chaotic Dynamics in Rational Polygonal Billiards

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2005
• Main Author: Kokshenev, V.B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209346
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Chaotic Dynamics in Rational Polygonal Billiards / V.B. Kokshenev // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 28 назв. — англ.

We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to the controversial issue of regular and irregular motion in polygons is taken within the alternative deterministic and stochastic frameworks. The analysis is developed in terms of the billiard-wall collision distribution and the particle survival probability, simulated in closed and weakly open polygons, respectively. In the multi-vertex polygons, the late-time wall-collision events result in circular-like, regular periodic trajectories (sliding orbits), which, in the open billiard case, are likely transformed into the surviving collective excitations (vortices). Having no topological analogy with the regular orbits in the geometrically corresponding circular billiard, sliding orbits and vortices are well distinguished in the weakly open polygons via the universal and non-universal relaxation dynamics.