A Poincaré-Birkhoff theorem for tight Reeb flows on \(S^3\)

DOI10.1007/s00222-014-0515-2zbMath1364.37077arXiv1110.3782OpenAlexW3105376079MaRDI QIDQ2257725

Pedro A. S. Salomão, Al Momin, Umberto L. Hryniewicz

Publication date: 2 March 2015

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3782

zbMATH Keywords

geodesic flowReeb flowPoincaré-Birkhoff theoremHopf linkresonance condition

Mathematics Subject Classification ID

Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Symplectic field theory; contact homology (53D42)

Related Items (17)

Elliptic bindings for dynamically convex Reeb flows on the real projective three-space ⋮ Positive topological entropy for Reeb flows on 3-dimensional Anosov contact manifolds ⋮ Closed Reeb orbits on the sphere and symplectically degenerate maxima ⋮ Dynamical convexity and elliptic periodic orbits for Reeb flows ⋮ Periodic and subharmonic solutions with winding number for \(p\)-Laplacian equations by the Poincaré-Birkhoff theorem ⋮ Refinements of Franks' theorem and applications in Reeb dynamics ⋮ Homological invariants of codimension 2 contact submanifolds ⋮ A symplectic dynamics proof of the degree-genus formula ⋮ Global diffusion on a tight three-sphere ⋮ Legendrian contact homology and topological entropy ⋮ The Conley conjecture and beyond ⋮ On reversible maps and symmetric periodic points ⋮ Systems of Transversal Sections near Critical Energy Levels of Hamiltonian Systems in ℝ⁴ ⋮ Global surfaces of section for dynamically convex Reeb flows on lens spaces ⋮ Controlled Reeb dynamics -- three lectures not in Cala Gonone ⋮ Reeb orbits that force topological entropy ⋮ Pseudorotations of the -disc and Reeb flows on the -sphere

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