On algebraically integrable outer billiards

TL;DR

This paper proves that if an outer billiard system around a plane oval exhibits a specific form of algebraic integrability, then the oval must necessarily be an ellipse, highlighting a unique geometric characterization.

Contribution

It establishes a rigidity result linking algebraic integrability of outer billiards to the oval being an ellipse, a novel geometric insight.

Findings

Outer billiard algebraic integrability implies the oval is an ellipse

Provides a characterization of ellipses via integrability properties

Strengthens understanding of billiard dynamics in convex shapes

Abstract

We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse.