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

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  • 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.
    Mathematics Subject Classification: Primary: 37J45; Secondary: 53D40.

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