Angular Billiard and Algebraic Birkhoff conjecture

TL;DR

This paper introduces the Angular billiard, a new dynamical system related to convex curves, and uses it to derive novel results concerning the algebraic Birkhoff conjecture on integrable billiards.

Contribution

The paper presents the Angular billiard system and demonstrates its duality with Birkhoff billiard, providing new insights into the algebraic Birkhoff conjecture.

Findings

Angular billiard acts on exterior points of convex curves.

The system is dual to Birkhoff billiard near the boundary.

New results on the algebraic Birkhoff conjecture are obtained.

Abstract

In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boundary curve this system turns out to be dual to the Birkhoff billiard. Using this system we get new results on algebraic Birkhoff conjecture on integrable billiards.