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Propagation in Hamiltonian dynamics and relative symplectic homology

Paul Biran·Leonid Polterovich·Dietmar Salamon
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Abstract

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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Paul Biran, Leonid Polterovich, Dietmar Salamon. 2001-08-20. Propagation in Hamiltonian dynamics and relative symplectic homology. https://arxiv.org/abs/math/0108134

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