Some remarks on periodic billiard orbits in rational polygons
Dynamical Systems
2016-09-06 v1
Abstract
A polygon is called rational if the angle between each pair of sides is a rational multiple of The main theorem we will prove is Theorem 1: For rational polygons, periodic points of the billiard flow are dense in the phase space of the billiard flow. This is a strengthening of Masur's theorem, who has shown that any rational polygon has ``many'' periodic billiard trajectories; more precisely, the set of directions of the periodic trajectories are dense in the set of velocity directions We will also prove some refinements of Theorem 1: the ``well distribution'' of periodic orbits in the polygon and the residuality of the points with a dense set of periodic directions.
Keywords
Cite
@article{arxiv.math/9408217,
title = {Some remarks on periodic billiard orbits in rational polygons},
author = {Michael Boshernitzan and G. A. Galperin and Tyll Krüger and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:math/9408217},
year = {2016}
}