A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows

Fonda, Alessandro; Ureña, Antonio J.

doi:10.1016/j.anihpc.2016.04.002

Fonda, Alessandro ; Ureña, Antonio J.

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 679-698.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2016.04.002

Mots clés : Poincaré–Birkhoff, Periodic solutions, Hamiltonian systems

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     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},
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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. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.04.002/

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