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 . 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