Propagation in Hamiltonian dynamics and relative symplectic homology

Paul Biran*, Leonid Polterovich, Dietmar Salamon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)65-118
Number of pages54
JournalDuke Mathematical Journal
Volume119
Issue number1
DOIs
StatePublished - 15 Jul 2003

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