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Noncontractible periodic orbits in cotangent bundles and Floer homology | | Joa Weber
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28 Oct 2004 | | Subject: | Symplectic Geometry; Dynamical Systems MSC-class: 37Jxx (Primary) 53D40 (Secondary) | math.SG math.DS | | Affiliation: | ETH-Zurich | | Abstract: | For every nontrivial free homotopy class $alpha$ of loops in every closed connected Riemannian manifold $M$, we prove existence of a noncontractible 1-periodic orbit, for every compactly supported time-dependent Hamiltonian on the open unit cotangent bundle which is sufficiently large over the zero section. The proof shows that the Biran-Polterovich-Salamon capacity is finite for every closed connected Riemannian manifold and every free homotopy class of loops. This implies a dense existence theorem for periodic orbits on level hypersurfaces and, consequently, a refined version of the Weinstein conjecture: Existence of closed characteristics (one associated to each nontrivial $alpha$) on hypersurfaces in $T^*M$ which are of contact type and contain the zero section. | | Source: | arXiv, math.SG/0410609 | | Services: | Forum | Review | PDF | Favorites | |
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