Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles

dc.creatorNiche, Cesar J.
dc.date2003-12-03
dc.date2004-08-24
dc.date.accessioned2026-07-07T05:03:30Z
dc.date.available2026-07-07T05:03:30Z
dc.descriptionFor 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.descriptionv2. 17 pages, 2 figures. Proof of Proposition 1 rewritten and corrected. One reference added
dc.identifierhttps://arxiv.org/abs/math/0312074
dc.identifierhttp://arxiv.org/abs/math/0312074
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69447
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject37J45; 53D40
dc.titleNon-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles
dc.typetext

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