[Un théorème de Poincaré–Birkhoff en plusieurs dimensions sans torsion monotone]
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.
Accepté le :
Publié le :
Alessandro Fonda 1 ; Antonio J. Ureña 2
@article{CRMATH_2016__354_5_475_0, author = {Alessandro Fonda and Antonio J. Ure\~na}, 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}, }
Alessandro Fonda; Antonio J. Ureña. A higher-dimensional Poincaré–Birkhoff theorem without monotone twist. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 475-479. doi : 10.1016/j.crma.2016.01.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.023/
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