Outer billiards and the pinwheel map | Zendy

Richard Evan Schwartz | Zendy

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Outer billiards and the pinwheel map

Author(s) -

Richard Evan Schwartz

Publication year - 2011

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2011.5.255

Subject(s) - regular polygon , mathematics , polygon (computer graphics) , equivalence (formal languages) , pure mathematics , geometry , computer science , telecommunications , frame (networking)

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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