Pure Mathematics: Angular Billiard and Algebraic Birkhoff conjecture

Professor Andrey Mironov (Novosibirsk State University) will present his research in pure mathematics.

We introduce a dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighbourhood 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. The results were obtained with Michael Bialy (Tel Aviv).