Outer Billiards with Contraction

Outer Billiards with Contraction: Regular Polygons

We study outer billiards with contraction outside regular polygons. For regular n-gons with n = 3, 4, 5, 6, 8, and 12, we show that as the contraction rate approaches 1, dynamics of the system converges, in a certain sense, to that of the usual outer billiards map. These are precisely the values of n ≥ 3 with [Q(e) : Q] ≤ 2. Then we discuss how such convergence may fail in the case of n = 7.

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Introducing projective billiards

We introduce and study a new class of dynamical systems, the projective billiards, associated with a smooth closed convex plane curve equipped with a smooth field of transverse directions. Projective billiards include the usual billiards along with the dual, or outer, billiards.

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Outer Billiards on Kites by

1 Preface Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B.H. Neumann introduced outer billiards in the 1950s, and J. Moser popularized outer billiards in the 1970s as a toy model for celestial mechanics. Outer billiards is an appealing dynamical system because of its simplicity and also because of its connection to such topics as interval exchange ...

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Outer Billiards on Kites by Richard Evan

1 Preface Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B.H. Neumann introduced outer billiards in the 1950s, and J. Moser popularized outer billiards in the 1970s as a toy model for celestial mechanics. Outer billiards is an appealing dynamical system because of its simplicity and also because of its connection to topics such as interval exchange ...

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Outer Billiards on Kites

1 Preface Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B.H. Neumann introduced outer billiards in the 1950s, and J. Moser popularized outer billiards in the 1970s as a toy model for celestial mechanics. Outer billiards is an appealing dynamical system because of its simplicity and also because of its connection to such topics as interval exchange ...

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Outer Billiards with Contraction

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