Dense existence of periodic Reeb orbits and ECH spectral invariants

2015/08/30 by Irie, Kei · 4 citations
#53D42 #70H12 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1508.07542

Abstract

In this paper, we prove (1): for any closed contact three-manifold with a C^∞-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a C^∞-generic Riemannian metric, the union of closed geodesics is dense. The key observation is C^∞-closing lemma for 3D Reeb flows, which follows from the fact that the embedded contact homology (ECH) spectral invariants recover the volume.

Cited by

• Strong closing lemmas in Hamiltonian dynamics
• Symplectic Weyl Laws
• Orbifold Floer spectral invariants, symmetric product links and Weyl laws
• Hamiltonian linking and Symplectic packing

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• Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy
• Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds