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Mathematics > Symplectic Geometry

arXiv:1805.02980 (math)
[Submitted on 8 May 2018]

Title:A Poincaré-Birkhoff theorem for Hamiltonian flows on nonconvex domains

Authors:Alessandro Fonda, Antonio J. Ureña
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Abstract:We present a higher-dimensional version of the Poincaré-Birkhoff theorem which applies to Poincaré time maps of Hamiltonian systems. The maps under consideration are neither required to be close to the identity nor to have a monotone twist. The annulus is replaced by the product of an $N$-dimensional torus and the interior of a $(N-1)$-dimensional (not necessarily convex) embedded sphere; on the other hand, the classical boundary twist condition is replaced by an avoiding rays condition.
Subjects: Symplectic Geometry (math.SG); Dynamical Systems (math.DS)
MSC classes: 34C25, 37J10
Cite as: arXiv:1805.02980 [math.SG]
  (or arXiv:1805.02980v1 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1805.02980
Related DOI: https://doi.org/10.13140/RG.2.2.11664.10241

Submission history

From: Antonio J. Urena [view email]
[v1] Tue, 8 May 2018 12:40:23 UTC (25 KB)
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