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 the controversial issue of regular and irregular motion in polygons is taken within the alternative deter...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2005 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209346 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-209346 |
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Kokshenev, V.B. 2025-11-19T12:25:57Z 2005 On Chaotic Dynamics in Rational Polygonal Billiards / V.B. Kokshenev // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 28 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37D45; 37D50; 51E12; 60C05; 60J60 https://nasplib.isofts.kiev.ua/handle/123456789/209346 https://doi.org/10.3842/SIGMA.2005.014 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. The financial support of the Brazilian agency CNPq is acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Chaotic Dynamics in Rational Polygonal Billiards Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Chaotic Dynamics in Rational Polygonal Billiards |
| spellingShingle |
On Chaotic Dynamics in Rational Polygonal Billiards Kokshenev, V.B. |
| title_short |
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_sort |
on chaotic dynamics in rational polygonal billiards |
| author |
Kokshenev, V.B. |
| author_facet |
Kokshenev, V.B. |
| publishDate |
2005 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209346 |
| citation_txt |
On Chaotic Dynamics in Rational Polygonal Billiards / V.B. Kokshenev // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 28 назв. — англ. |
| work_keys_str_mv |
AT kokshenevvb onchaoticdynamicsinrationalpolygonalbilliards |
| first_indexed |
2025-12-07T18:00:02Z |
| last_indexed |
2025-12-07T18:00:02Z |
| _version_ |
1850886066710511616 |