Outer Billiards and the Pinwheel Map

Details Outer Billiards and the Pinwheel Map Outer Billiards and the Pinwheel Map

2010-04-18

arxiv.org/abs/1004.3025v2

Mathematics

Dynamical Systems

54 pages. latest version corrects some typos in previous version

Scientific paper

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.

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