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Periods of Pseudo-Integrable Billiards

Periods of Pseudo-Integrable Billiards Consider billiard desks composed of two concentric half-circles connected with two edges. We examine billiard trajectories having a fixed circle concentric with the boundary semicircles as the caustic, such that the rotation numbers with respect to the half-circles are $$\rho _1$$ ρ 1 and $$\rho _2$$ ρ 2 respectively. Are such billiard trajectories periodic, and what are all possible periods for given $$\rho _1$$ ρ 1 and $$\rho _2$$ ρ 2 ?. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Periods of Pseudo-Integrable Billiards

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Mathematical Physics; Analysis; Dynamical Systems and Ergodic Theory; Combinatorics
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-014-0004-0
Publisher site
See Article on Publisher Site

Abstract

Consider billiard desks composed of two concentric half-circles connected with two edges. We examine billiard trajectories having a fixed circle concentric with the boundary semicircles as the caustic, such that the rotation numbers with respect to the half-circles are $$\rho _1$$ ρ 1 and $$\rho _2$$ ρ 2 respectively. Are such billiard trajectories periodic, and what are all possible periods for given $$\rho _1$$ ρ 1 and $$\rho _2$$ ρ 2 ?.

Journal

Arnold Mathematical Journal – Springer Journals

Published: Jan 21, 2015

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