On Chaotic Dynamics in Rational Polygonal Billiards
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 controversial issue of regular and irregular motion in polygons is taken within the alternative determini...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2005-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://www.emis.de/journals/SIGMA/2005/Paper014/ |
| _version_ | 1811234260329168896 |
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| author | Valery Kokshenev |
| author_facet | Valery Kokshenev |
| author_sort | Valery Kokshenev |
| collection | DOAJ |
| description | 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 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 the 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. |
| first_indexed | 2024-04-12T11:33:43Z |
| format | Article |
| id | doaj.art-e2725c4d4d1e44c7b17971306a938650 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-12T11:33:43Z |
| publishDate | 2005-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-e2725c4d4d1e44c7b17971306a9386502022-12-22T03:34:55ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592005-11-011014On Chaotic Dynamics in Rational Polygonal BilliardsValery KokshenevWe 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 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 the 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.http://www.emis.de/journals/SIGMA/2005/Paper014/polygonshyperbolic systems with singularitiesstochastic systemchaotic dynamicsanomalous diffusion process |
| spellingShingle | Valery Kokshenev On Chaotic Dynamics in Rational Polygonal Billiards Symmetry, Integrability and Geometry: Methods and Applications polygons hyperbolic systems with singularities stochastic system chaotic dynamics anomalous diffusion process |
| title | On Chaotic Dynamics in Rational Polygonal Billiards |
| title_full | On Chaotic Dynamics in Rational Polygonal Billiards |
| title_fullStr | On Chaotic Dynamics in Rational Polygonal Billiards |
| title_full_unstemmed | On Chaotic Dynamics in Rational Polygonal Billiards |
| title_short | On Chaotic Dynamics in Rational Polygonal Billiards |
| title_sort | on chaotic dynamics in rational polygonal billiards |
| topic | polygons hyperbolic systems with singularities stochastic system chaotic dynamics anomalous diffusion process |
| url | http://www.emis.de/journals/SIGMA/2005/Paper014/ |
| work_keys_str_mv | AT valerykokshenev onchaoticdynamicsinrationalpolygonalbilliards |