Mathematics

We present a Hamiltonian normal form for a charged particle moving on a closed surface under the effect of a strong magnetic field. We apply the normal form in order to: A) trap the particle inside some regions via the KAM theorem; B) prove the existence of periodic orbits; C) show that the motion is periodic for every initial condition if and only if the magnetic field is constant and the surface has constant curvature. This is joint work with Luca Asselle.