2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60270For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.19 pages, 1 figureDifferential GeometryDynamical SystemsSymplectic Geometry58F05(primary), 58F22(secondary)text