Introducing symplectic billiards

TL;DR

This paper introduces symplectic billiards, a new dynamical system where symplectic area replaces length as the generating function, highlighting its properties and differences from traditional billiards.

Contribution

It presents the concept of symplectic billiards, a novel variation of billiard systems, and explores its fundamental properties and distinctions from Birkhoff billiards.

Findings

Symplectic billiards use symplectic area as the generating function.

Basic properties of symplectic billiards are established.

Differences between symplectic and Birkhoff billiards are analyzed.

Abstract

In this article we introduce a simple dynamical system called symplectic billiards. As opposed to usual/Birkhoff billiards, where length is the generating function, for symplectic billiards symplectic area is the generating function. We explore basic properties and exhibit several similarities, but also differences of symplectic billiards to Birkhoff billiards.