Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles
| dc.creator | Niche, Cesar J. | |
| dc.date | 2003-12-03 | |
| dc.date | 2004-08-24 | |
| dc.date.accessioned | 2026-07-07T05:03:30Z | |
| dc.date.available | 2026-07-07T05:03:30Z | |
| dc.description | For many classes of symplectic manifolds, the Hamiltonian flow of a function with sufficiently large variation must have a fast periodic orbit. This principle is the base of the notion of Hofer-Zehnder capacity and some other symplectic invariants and leads to numerous results concerning existence of periodic orbits of Hamiltonian flows. Along these lines, we show that given a negatively curved manifold M, a neigbhourhood U of M in the cotangent bundle, a sufficiently small magnetic field and a non-trivial free homotopy class of loops, then the magnetic flow of a Hamiltonian with big enough variation has a one-periodic orbit in that class. As a consequence, we obtain estimates for the relative Hofer-Zehnder capacity and the Biran-Polterovich-Salamon capacity of a neighbourhood of M. | |
| dc.description | v2. 17 pages, 2 figures. Proof of Proposition 1 rewritten and corrected. One reference added | |
| dc.identifier | https://arxiv.org/abs/math/0312074 | |
| dc.identifier | http://arxiv.org/abs/math/0312074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69447 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 37J45; 53D40 | |
| dc.title | Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles | |
| dc.type | text |