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.
| Original language | English |
|---|---|
| Pages (from-to) | 1191-1211 |
| Number of pages | 21 |
| Journal | Annales Henri Lebesgue |
| Volume | 5 |
| DOIs | |
| Publication status | Published - 2022 |
| Externally published | Yes |
Funding
L.A. is partially supported by the Deutsche Forschungsgemeinschaft under the DFG-grant 380257369 (Morse theoretical methods in Hamiltonian dynamics). G.B. is partially supported by the Deutsche Forschungsgemeinschaft under Germany\u2019s Excellence Strategy EXC2181/1- 390900948 (the Heidelberg STRUCTURES Excellence Cluster), the Collaborative Research Center SFB/TRR 191- 281071066 (Symplectic Structures in Geometry, Algebra and Dynamics), and the Research Training Group RTG 2229- 281869850 (Asymptotic Invariants and Limits of Groups and Spaces).
| Funders | Funder number |
|---|---|
| Deutsche Forschungsgemeinschaft | RTG 2229 - 281869850, 281071066, 380257369, EXC2181/1 - 390900948 |
Keywords
- Magnetic systems
- trapping regions
- KAM tori
- periodic orbits
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