Counting Collisions in an 𝑁-Billiard System Using Angles Between Collision Subspaces

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dc.contributor.authorGasiorek, Sean
dc.date.accessioned2025-12-22T09:21:07Z
dc.date.issued2020
dc.description.abstractThe principal angles between binary collision subspaces in an 𝑁-billiard system in 𝒹-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.
dc.description.sponsorshipThe 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.
dc.identifier.citationCounting Collisions in an 𝑁-Billiard System Using Angles Between Collision Subspaces. Sean Gasiorek. SIGMA 16 (2020), 119, 13 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.119
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 37J37; 70F99; 55R80; 70F16
dc.identifier.otherarXiv:1810.05777
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211001
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleCounting Collisions in an 𝑁-Billiard System Using Angles Between Collision Subspaces
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік