## Abstract

We consider magnetic Tonelli Hamiltonian systems on the cotangent bundle of the 2-sphere, where the magnetic form is not necessarily exact. It is known that, on very low and on high energy levels, these systems may have only finitely many periodic orbits. Our main result asserts that almost all energy levels in a precisely characterized intermediate range (e(0), e(1)) possess infinitely many periodic orbits. Such a range of energies is non-empty, for instance, in the physically relevant case where the Tonelli Lagrangian is a kinetic energy and the magnetic form is oscillating (in which case, e(0) = 0 is the minimal energy of the system).

Original language | English |
---|---|

Pages (from-to) | 17-30 |

Number of pages | 14 |

Journal | Advanced Nonlinear Studies |

Volume | 17 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2 Jan 2017 |

## Keywords

- Tonelli Lagrangians
- Magnetic Flows
- Hamiltonian Systems
- Periodic Orbits
- Mane Critical Values
- LAGRANGIAN SYSTEMS
- GEODESICS
- SURFACES
- FIELDS
- Mañé Critical Values