Magnetic Katok Examples on the two-sphere

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 ${\mathbb{C}}^2$. Our construction generalizes the examples of integrable Finsler metrics on the two-sphere with only two closed geodesics due to A. Katok.

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

Cited by in corpus (4)

• Reeb dynamics inspired by Katok's example in Finsler geometry
• Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
• On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
• On the rigidity of Zoll magnetic systems on surfaces