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- W2950124879 abstract "In this long paper we give a fairly complete analysis of outer billiards on the Penrose kite. Our analysis reveals that this 2-dimensional non-compact system has a 3-dimensional compactification, a certain polyhedron exchange map, and that this compactification has a renormalization scheme. These two features allow us to make some sharp statements concerning the distribution, large-scale geometry, fine-scale geometry, and hidden algebraic symmetries of the orbits. For instance, one of our results is that the union of the unbounded orbits has Hausdorff dimension 1. We give a computer-aided proof of the results concerning the compactification and the renormalization. This proof involves finitely many calculations done with exact integer arithmetic." @default.
- W2950124879 created "2019-06-27" @default.
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- W2950124879 date "2011-02-22" @default.
- W2950124879 modified "2023-09-27" @default.
- W2950124879 title "Outer Billiards on the Penrose Kite: Compactification and Renormalizaiton" @default.
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