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Outer billiards and the pinwheel map

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  • In this paper we establish an equivalence between an outer billiards system based on a convex polygon $P$ and an auxiliary system, which we call the pinwheel map, that is based on $P$ in a different way. The pinwheel map is akin to a first-return map of the outer billiards map. The virtue of our result is that most of the main questions about outer billiards can be formulated in terms of the pinwheel map, and the pinwheel map is simpler and seems more amenable to fruitful analysis.
    Mathematics Subject Classification: Primary: 37E15; Secondary: 37E99.


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