English

Magnetic Katok Examples on the two-sphere

Symplectic Geometry 2018-05-16 v2 Dynamical Systems

Abstract

We show that there exist non-exact magnetic flows on the two-sphere having an energy level whose double cover is strictly contactomorphic to an irrational ellipsoid in C2\mathbb C^2. Our construction generalizes the examples of integrable Finsler metrics on the two-sphere with only two closed geodesics due to A. Katok.

Cite

@article{arxiv.1507.05341,
  title  = {Magnetic Katok Examples on the two-sphere},
  author = {Gabriele Benedetti},
  journal= {arXiv preprint arXiv:1507.05341},
  year   = {2018}
}

Comments

13 pages. Second version. We have added a sharper example in the larger class of Lagrangians attaining a Morse-Bott non-degenerate minimum at the zero section. Comments, questions, and suggestions are very welcome. To appear in the Bulletin of the London Mathematical Society

R2 v1 2026-06-22T10:14:42.865Z