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arXiv · 2104.06733

Non-resonant circles for strong magnetic fields on surfaces

L. Asselle·G. Benedetti
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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.

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L. Asselle, G. Benedetti. 2021-04-14. Non-resonant circles for strong magnetic fields on surfaces. https://arxiv.org/abs/2104.06733

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