Asymptotic periodicity in outer billiards with contraction

Outer Billiards with Contraction

We study the dynamics of outer billiards with contraction outside polygons. The dynamics can be either regular or chaotic, depending on the parameters.

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.

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 ...

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 ...

8 Outer Billiards on Kites