A Reeb flow on the three-sphere without a disk-like global surface of Section

DOI10.1007/s12346-020-00368-3zbMath1437.53059arXiv1902.01172OpenAlexW3004626543MaRDI QIDQ2301844

Otto van Koert

Publication date: 25 February 2020

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.01172

zbMATH Keywords

integrable systemsReeb flowsglobal surfaces of section

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Contact manifolds (general theory) (53D10) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (7)

Global surfaces of Section with positive genus for dynamically convex Reeb flows ⋮ Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere ⋮ Genus zero global surfaces of section for Reeb flows and a result of Birkhoff ⋮ A symplectic dynamics proof of the degree-genus formula ⋮ Reeb flows without simple global surfaces of section ⋮ Surfaces of Section for Seifert fibrations ⋮ Reeb flows, pseudo-holomorphic curves and transverse foliations

Cites Work

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• On the existence of disk-like global sections for Reeb flows on the tight 3-sphere
• Contact surgery and symplectic handlebodies
• Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
• The dynamics on three-dimensional strictly convex energy surfaces
• A smooth counterexample to the Seifert conjecture
• On properties of Bourgeois contact structures
• Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere
• Lecture notes on stabilization of contact open books
• An Introduction to Contact Topology

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