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arXiv · 1805.02980

A Poincaré-Birkhoff theorem for Hamiltonian flows on nonconvex domains

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.

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Alessandro Fonda, Antonio J. Ureña. 2018-05-08. A Poincaré-Birkhoff theorem for Hamiltonian flows on nonconvex domains. https://doi.org/10.13140/rg.2.2.11664.10241

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