On the existence of periodic orbits for magnetic systems on the two-sphere

Abstract

We prove that there exist periodic orbits on almost all compact regular energy levels of a Hamiltonian function defined on a twisted cotangent bundle over the two-sphere. As a corollary, given any Riemannian two-sphere and a magnetic field on it, there exists a closed magnetic geodesic for almost all kinetic energy levels.

arXiv commentNew title and abstract; same content; to appear in J. Mod. Dyn

References in corpus (6)

• Symplectic topology of Mañé's critical values
• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
• Closed orbits of a charge in a weakly exact magnetic field
• Hofer-Zehnder capacity and length minimizing Hamiltonian paths
• Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level
• Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits

Cited by in corpus (7)

• The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles
• On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
• Periodic orbits in virtually contact structures
• Two constructions of virtually contact structures
• Symplectic fillings of unit cotangent bundles of hyperbolic surfaces
• On an integrable magnetic geodesic flow on the two-torus
• On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces