Polygonal symplectic billiards

Abstract

In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their properties and derive various conjectures using two numerical implementations.

Extremal Area Of Polygons Sliding Along Curves

“…In section 8.3 we discuss the relation between closed orbits of symplectic billiards and critical points of the inner area function A on convex curves. The case that this curve is a polygon is systematic studied in [2]. They obtain new results, some of which are inspired by numerical investigations.…”

Open Problems on Billiards and Geometric Optics

“…Similarly one defines polygonal symplectic billiards. In [1,2], a number of polygons are described that have the property that all symplectic billiard orbits are periodic (in particular, the affine-regular polygons and the trapezoids have this property).…”