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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2020
Автор: Gasiorek, Sean
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2020
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211001
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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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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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