Non-Contractible Periodic Orbits In Hamiltonian Dynamics On Closed Symplectic Manifolds

Keywords

augmented action; Floer homology; Hamiltonian flows; non-contractible periodic orbits

Abstract

We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a closed toroidally monotone or toroidally negative monotone symplectic manifold implies the existence of infinitely many non-contractible periodic orbits in a specific collection of free homotopy classes. The main new ingredient in the proofs of these results is a filtration of Floer homology by the so-called augmented action. This action is independent of capping and, under favorable conditions, the augmented action filtration for toroidally (negative) monotone manifolds can play the same role as the ordinary action filtration for atoroidal manifolds.

Publication Date

9-1-2016

Publication Title

Compositio Mathematica

Volume

152

Issue

9

Number of Pages

1777-1799

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1112/S0010437X16007508

Socpus ID

84975114133 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84975114133

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