Propagation in Hamiltonian dynamics and relative symplectic homology

Details Propagation in Hamiltonian dynamics and relative symplectic homology Propagation in Hamiltonian dynamics and relative symplectic homology

2001-08-20

arxiv.org/abs/math/0108134v1

Mathematics

Symplectic Geometry

58 pages, 2 figures

Scientific paper

The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating Hamiltonian is sufficiently large over the zero section. The proof is based on Floer homology and on the notion of a relative symplectic capacity. Applications include results about propagation properties of sequential Hamiltonian systems, periodic orbits on hypersurfaces, Hamiltonian circle actions, and smooth Lagrangian skeletons in Stein manifolds.

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