Algebraic non-integrability of magnetic billiards

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece of the boundary must be algebraic and satisfies very strong restrictions. In particular in the case of ellipse it follows that magnetic billiard is algebraically not integrable for all magnitudes of the magnetic field. Results were obtained with Michael Bialy (Tel Aviv).