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.
@article{AIHPC_2017__34_3_679_0, 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}, number = {3}, year = {2017}, doi = {10.1016/j.anihpc.2016.04.002}, mrnumber = {3633740}, zbl = {1442.37076}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2016.04.002/} }
TY - JOUR AU - Fonda, Alessandro AU - Ureña, Antonio J. TI - A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 679 EP - 698 VL - 34 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2016.04.002/ DO - 10.1016/j.anihpc.2016.04.002 LA - en ID - AIHPC_2017__34_3_679_0 ER -
%0 Journal Article %A Fonda, Alessandro %A Ureña, Antonio J. %T A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 679-698 %V 34 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2016.04.002/ %R 10.1016/j.anihpc.2016.04.002 %G en %F AIHPC_2017__34_3_679_0
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://www.numdam.org/articles/10.1016/j.anihpc.2016.04.002/
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