Speaker
Prof.
Vivina Barutello
(Università di Torino)
Description
We study the integrability of Kepler billiards, mechanical systems in which a particle moves under the influence of a Keplerian potential and undergoes elastic reflections at the boundary of a strictly convex planar domain with smooth boundary. We prove that, with the possible exception of a single position of the gravitational center, analytic integrability at any energy regime can occur only when the domain is an ellipse and the center is located at one of its foci. This result provides a partial affirmative answer to the Keplerian counterpart of the classical Birkhoff–Poritsky Conjecture. This research is in collaboration with S. Baranzini, I. De Blasi and S. Terracini.