Non-resonant circles for strong magnetic fields on surfaces
Dynamical Systems
2021-04-15 v1 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2104.06733,
title = {Non-resonant circles for strong magnetic fields on surfaces},
author = {L. Asselle and G. Benedetti},
journal= {arXiv preprint arXiv:2104.06733},
year = {2021}
}
Comments
13 Pages, Comments welcome