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• W2063194496 abstract "We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case." @default.
• W2063194496 created "2016-06-24" @default.
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• W2063194496 date "2012-06-01" @default.
• W2063194496 modified "2023-10-14" @default.
• W2063194496 title "Classification of symmetric periodic trajectories in ellipsoidal billiards" @default.
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• W2063194496 doi "https://doi.org/10.1063/1.4706003" @default.
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