Outer billiard outside regular polygons

Outer billiard outside regular polygons

We consider the outer billiard outside a regular convex polygon. We deal with the case of regular polygons with 3, 4, 5, 6 or 10 sides. We describe the symbolic dynamics of the map and compute the complexity of the language.

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.

Stable Billiard Paths on Polygons

Periodic Orbits in Outer Billiard

It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided the boundary is not a parallelogram.

Recurrence and Periodic Billiard Orbits in Polygons

We show that almost all billiard trajectories return parallel to themselves for rank 1, ergodic polygons. Applications are given to the existence of periodic trajectories.