English

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

R2 v1 2026-06-24T01:09:19.486Z