Outer billiard outside regular polygons

TL;DR

This paper studies the outer billiard map outside regular convex polygons with 3, 4, 5, 6, and 10 sides, analyzing its symbolic dynamics and complexity of the generated language.

Contribution

It provides a detailed description of the symbolic dynamics and computes the complexity for outer billiard outside specific regular polygons, extending understanding of these dynamical systems.

Findings

Symbolic dynamics characterized for each polygon type.

Complexity functions computed for the language of the system.

Insights into the dynamical behavior outside regular polygons.

Abstract

We consider outer billiard outside regular convex polygons. We deal with the case of regular polygons with $\{3,4,5,6,10\}$ sides, and we describe the symbolic dynamics of the map and compute the complexity of the language.