We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a corollary, there exist infinitely many periodic magnetic geodesics for every low speed in the following cases: i) the surface is not the two-sphere, ii) the magnetic field vanishes somewhere.
NON-RESONANT CIRCLES FOR STRONG MAGNETIC FIELDS ON SURFACES / Asselle, L.; Benedetti, G.. - In: ANNALES HENRI LEBESGUE. - ISSN 2644-9463. - 5:(2022), pp. 1191-1211. [10.5802/ahl.147]
NON-RESONANT CIRCLES FOR STRONG MAGNETIC FIELDS ON SURFACES
ASSELLE L.;BENEDETTI G.
2022-01-01
Abstract
We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a corollary, there exist infinitely many periodic magnetic geodesics for every low speed in the following cases: i) the surface is not the two-sphere, ii) the magnetic field vanishes somewhere.File in questo prodotto:
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