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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 119, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.119 (Mi sigma1657) 		 
Counting Collisions in an $N$-Billiard System Using Angles Between Collision Subspaces

Sean Gasiorek

School of Mathematics and Statistics, Carslaw F07, University of Sydney, NSW 2011, Australia
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DOI: https://doi.org/10.3842/SIGMA.2020.119
Abstract: The 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.
Keywords: mathematical billiards, angles between subspaces, counting collisions.
Funding agency Grant number
National Science Foundation DMS-1440140
Australian Research Council DP190101838
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.
Received: July 24, 2020; in final form November 10, 2020; Published online November 21, 2020
Bibliographic databases:
Document Type: Article
MSC: 37J37, 70F99, 55R80, 70F16
Language: English
Citation: Sean Gasiorek, “Counting Collisions in an $N$-Billiard System Using Angles Between Collision Subspaces”, SIGMA, 16 (2020), 119, 13 pp.
Citation in format AMSBIB
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