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arXiv · 1503.09035

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

Gabriele Benedetti·Kai Zehmisch
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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.

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Gabriele Benedetti, Kai Zehmisch. 2015-03-31. On the existence of periodic orbits for magnetic systems on the two-sphere. https://doi.org/10.3934/jmd.2015.9.141

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