On Non-contractible Periodic Orbits of Hamiltonian Diffeomorphisms

2012/10/15 by Basak Z. Gurel · 2 citations
Mathematics · #math.SG #math.DS

paper · pdf · doi:10.1112/blms/bdt051

9 pages

arxiv created 2012/10/15 · arxiv updated 2014/02/26

Abstract

We prove that any Hamiltonian diffeomorphism of a closed symplectic manifold equipped with an atoroidal symplectic form has simple non-contractible periodic orbits of arbitrarily large period, provided that the diffeomorphism has a non-degenerate (or even isolated and homologically non-trivial) periodic orbit with non-zero homology class and the set of one-periodic orbits in that class is finite.

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• Open problems in billiards and quantitative symplectic geometry
• On the growth rate of Reeb orbit on star-shaped hypersurfaces

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