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- W2058413963 abstract "We give a fairly complete analysis of outer billiards on the Penrosekite. Our analysis reveals that this $2$-dimensional dynamical systemhas a $3$-dimensional compactification, a certain polyhedron exchangemap defined on the $3$-torus, and that this $3$-dimensional systemadmits a renormalization scheme. The two features allow us to makesharp statements concerning the distribution, large- and fine-scalegeometry, and hidden algebraic symmetry, of the orbits. One concreteresult is that the union of the unbounded orbits has Hausdorffdimension $1$. We establish many of the results with computer-aidedproofs that involve only integer arithmetic." @default.
- W2058413963 created "2016-06-24" @default.
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- W2058413963 date "2011-01-01" @default.
- W2058413963 modified "2023-10-02" @default.
- W2058413963 title "Outer billiards on the Penrose kite: Compactification and renormalization" @default.
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- W2058413963 doi "https://doi.org/10.3934/jmd.2011.5.473" @default.
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