Title: Introducing symplectic billiards,
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.