Unbounded Orbits for Outer Billiards

By Richard Evan Schwartz. 2007

52 citations recorded by the source corpus.

The question of B.H. Neumann, which dates back to the 1950s, asks if there exists an outer billiards system with an unbounded orbit. We prove that outer billiards for the Penrose kite, the convex quadrilateral from the Penrose tiling, has an unbounded orbit. We also analyze some finer properties of the orbit structure, and in particular produce an uncountable family of unbounded orbits. Our methods relate outer billiards on the Penrose kite to polygon exchange maps, arithmetic dynamics, and self-similar tilings.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ccc57ff0236a6d2d699befd0cf027215c4e80c0

How researchers see this paper

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In Geometry and Topology

1. Richard Evan Schwartz
2. Anna Pratoussevitch
3. Elisha Falbel
4. Serge Tabachnikov
5. Martin Deraux
6. Misha Bialy

In Mathematical Physics

1. Richard Evan Schwartz
2. Elisha Falbel
3. Anna Pratoussevitch
4. Martin Deraux

Citations in the corpus

• Outer Billiards on Kites (2007, methodology): “tely, I am trying to verify the structure I noticed onthe computer, andso onemight expect there tobe some computation in the proof. The proof here uses considerably less computation than the proof in [S], but I still use a computer-aided proof in several places. For example, I use the computer to ch”