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

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In 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.
34 pages, 2 figures

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Symplectic Geometry, Dynamical Systems, 53D40; 37J45; 70H12

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http://salesiana.dossiersoluciones.com/handle/123456789/128878

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.1818
 http://arxiv.org/abs/0705.1818

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arXiv