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.
On the existence of periodic orbits for magnetic systems on the two-sphere / Benedetti, G.; Zehmisch, K.. - In: JOURNAL OF MODERN DYNAMICS. - ISSN 1930-5311. - 9:2(2015), pp. 141-146. [10.3934/jmd.2015.9.141]
On the existence of periodic orbits for magnetic systems on the two-sphere
Benedetti G.;
2015-01-01
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.File in questo prodotto:
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