Nous fournissons une preuve simple d'une version en plusieurs dimensions du théorème de Poincaré–Birkhoff qui s'applique aux applications de Poincaré des systèmes hamiltoniens. Ces applications ne sont tenues, ni d'être proches de l'identité, ni d'avoir une torsion monotone.
We provide a simple proof for a higher-dimensional version of the Poincaré–Birkhoff theorem, which applies to Poincaré time maps of Hamiltonian systems. These maps are required neither to be close to the identity nor to have a monotone twist.
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@article{CRMATH_2016__354_5_475_0, author = {Fonda, Alessandro and Ure\~na, Antonio J.}, title = {A higher-dimensional {Poincar\'e{\textendash}Birkhoff} theorem without monotone twist}, journal = {Comptes Rendus. Math\'ematique}, pages = {475--479}, publisher = {Elsevier}, volume = {354}, number = {5}, year = {2016}, doi = {10.1016/j.crma.2016.01.023}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2016.01.023/} }
TY - JOUR AU - Fonda, Alessandro AU - Ureña, Antonio J. TI - A higher-dimensional Poincaré–Birkhoff theorem without monotone twist JO - Comptes Rendus. Mathématique PY - 2016 SP - 475 EP - 479 VL - 354 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.01.023/ DO - 10.1016/j.crma.2016.01.023 LA - en ID - CRMATH_2016__354_5_475_0 ER -
%0 Journal Article %A Fonda, Alessandro %A Ureña, Antonio J. %T A higher-dimensional Poincaré–Birkhoff theorem without monotone twist %J Comptes Rendus. Mathématique %D 2016 %P 475-479 %V 354 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.01.023/ %R 10.1016/j.crma.2016.01.023 %G en %F CRMATH_2016__354_5_475_0
Fonda, Alessandro; Ureña, Antonio J. A higher-dimensional Poincaré–Birkhoff theorem without monotone twist. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 475-479. doi : 10.1016/j.crma.2016.01.023. http://www.numdam.org/articles/10.1016/j.crma.2016.01.023/
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