A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 679-698

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We propose an extension to higher dimensions of the Poincaré–Birkhoff Theorem which applies to Poincaré time-maps of Hamiltonian systems. Examples of applications to pendulum-type systems and weakly-coupled superlinear systems are also given.

DOI : 10.1016/j.anihpc.2016.04.002
Keywords: Poincaré–Birkhoff, Periodic solutions, Hamiltonian systems
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     author = {Fonda, Alessandro and Ure\~na, Antonio J.},
     title = {A higher dimensional {Poincar\'e{\textendash}Birkhoff} theorem for {Hamiltonian} flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {679--698},
     publisher = {Elsevier},
     volume = {34},
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     year = {2017},
     doi = {10.1016/j.anihpc.2016.04.002},
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Fonda, Alessandro; Ureña, Antonio J. A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 679-698. doi: 10.1016/j.anihpc.2016.04.002

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