Periodic magnetic flows on the two-torus

Speaker. Gabriele Benedetti
Date. 26.03.24 at 15:30

Abstract. An old problem in classical mechanics is the existence of periodic flows within specific classes of Hamiltonian systems such as geodesic and magnetic flows, and central forces. While only trivial examples of periodic flows among magnetic and central systems exist, Zoll and, later, Guillemin have shown that there are many exotic examples among geodesic flows on the two-sphere. Following Guillemin’s approach, the goal of this talk is to show how the Nash–Moser implicit function theorem can be applied to construct magnetic flows on the two-torus which are periodic for just one single value of the energy. This is joint work with Luca Asselle and Massimiliano Berti.