Periodic Orbits of Twisted Geodesic Flows and The Weinstein-Moser Theorem

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dc.creatorGinzburg, Viktor L.
dc.creatorGurel, Basak Z.
dc.date2007-05-13
dc.date.accessioned2026-07-07T08:01:20Z
dc.date.available2026-07-07T08:01:20Z
dc.descriptionIn this paper, we establish the existence of periodic orbits of a twisted geodesic flow on all low energy levels and in all dimensions whenever the magnetic field form is symplectic and spherically rational. This is a consequence of a more general theorem concerning periodic orbits of autonomous Hamiltonian flows near Morse-Bott non-degenerate, symplectic extrema. Namely, we show that all energy levels near such extrema carry periodic orbits, provided that the ambient manifold meets certain topological requirements. This result is a partial generalization of the Weinstein-Moser theorem. The proof of the generalized Weinstein-Moser theorem is a combination of a Sturm-theoretic argument and a Floer homology calculation.
dc.description34 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0705.1818
dc.identifierhttp://arxiv.org/abs/0705.1818
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128878
dc.subjectSymplectic Geometry
dc.subjectDynamical Systems
dc.subject53D40; 37J45; 70H12
dc.titlePeriodic Orbits of Twisted Geodesic Flows and The Weinstein-Moser Theorem
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