Outer Billiards and the Pinwheel Map
Dynamical Systems
2010-04-26 v2
Abstract
In this paper we establish a kind of bijection between the orbits of a polygonal outer billiards system and the orbits of a related (and simpler to analyze) system called the pinwheel map. One consequence of the result is that the outer billiards system has unbounded orbits if and only if the pinwheel map has unbounded orbits. As the pinwheel map is much easier to analyze directly, we think that this bijection will be helpful in attacking some of the main questions about polyonal outer billiards.
Cite
@article{arxiv.1004.3025,
title = {Outer Billiards and the Pinwheel Map},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:1004.3025},
year = {2010}
}
Comments
54 pages. latest version corrects some typos in previous version