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- Title
Periodic orbits for exact magnetic flows on surfaces.
- Authors
Contreras, Gonzalo; Macarini, Leonardo; Paternain, Gabriel P.
- Abstract
We show that any exact magnetic flow on a closed surface has periodic orbits in all energy levels. Moreover, we give homological and homotopical properties of these periodic orbits in terms of the Mañé's critical values of the corresponding Lagrangian. We also prove that if M is not the 2-torus, the energy level k is of contact type if and only if k > c0, where c0 is Mañé's strict critical value. When M is the 2-torus, we give examples for which the energy level c0 is of contact type.
- Subjects
COMBINATORIAL dynamics; MAGNETICS; LAGRANGIAN functions; DYNAMICAL systems; MATHEMATICS
- Publication
IMRN: International Mathematics Research Notices, 2004, Vol 2004, Issue 8, p361
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1155/S1073792804205050