Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces
The principal angles between binary collision subspaces in an -billiard system in -dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of collisions in the planar 3-billiard system problem. Comparison of thi...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211001 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces. Sean Gasiorek. SIGMA 16 (2020), 119, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862703928339070976 |
|---|---|
| author | Gasiorek, Sean |
| author_facet | Gasiorek, Sean |
| citation_txt | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces. Sean Gasiorek. SIGMA 16 (2020), 119, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The principal angles between binary collision subspaces in an -billiard system in -dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of collisions in the planar 3-billiard system problem. Comparison of this result with known billiard collision bounds in lower dimensions is discussed.
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| first_indexed | 2026-03-18T18:20:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211001 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T18:20:22Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gasiorek, Sean 2025-12-22T09:21:07Z 2020 Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces. Sean Gasiorek. SIGMA 16 (2020), 119, 13 pages 1815-0659 2020 Mathematics Subject Classification: 37J37; 70F99; 55R80; 70F16 arXiv:1810.05777 https://nasplib.isofts.kiev.ua/handle/123456789/211001 https://doi.org/10.3842/SIGMA.2020.119 The principal angles between binary collision subspaces in an -billiard system in -dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of collisions in the planar 3-billiard system problem. Comparison of this result with known billiard collision bounds in lower dimensions is discussed. The author is grateful for the detailed comments and suggestions of the referees. This material is based upon work supported by the National Science Foundation under Grant # DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2018 semester. This work was also supported by Discovery Project # DP190101838, Billiards within confocal quadrics and beyond, from the Australian Research Council. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces Article published earlier |
| spellingShingle | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces Gasiorek, Sean |
| title | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces |
| title_full | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces |
| title_fullStr | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces |
| title_full_unstemmed | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces |
| title_short | Counting Collisions in an -Billiard System Using Angles Between Collision Subspaces |
| title_sort | counting collisions in an -billiard system using angles between collision subspaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211001 |
| work_keys_str_mv | AT gasioreksean countingcollisionsinanbilliardsystemusinganglesbetweencollisionsubspaces |