Non-existence of global transverse Poincaré sections

DOI10.1016/j.geomphys.2021.104168zbMath1475.37065arXiv1905.10633OpenAlexW3136559654MaRDI QIDQ2032668

Roisin Braddell

Publication date: 14 June 2021

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.10633

zbMATH Keywords

energy surfacessurfaces of sectioncosymplectic geometry

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

• Codimension one symplectic foliations and regular Poisson structures
• A systolic inequality for geodesic flows on the two-sphere
• Topology of co-symplectic/co-Kähler manifolds
• A note on the symplectic topology of \(b\)-manifolds
• Global surfaces of section in the planar restricted 3-body problem
• On fibering certain foliated manifolds over \(S^1\)
• Complete Poincare sections and tangent sets
• Topology of energy surfaces and existence of transversal Poincaré sections
• On some new long periodic solutions of the plane restricted three body problem

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