Nous nous proposons de comparer deux capacités dans définies par les orbites périodiques de systèmes hamiltoniens. La première est la capacité de Floer-Hofer, issue de l’homologie symplectique ; la seconde est la capacité de Viterbo basée sur des fonctions génératrices. Nous montrons que la capacité intérieure de Floer-Hofer n’est pas plus grande que celle de Viterbo et qu’elles coïncident sur les ouverts dont le bord est une variété de contact restreinte. Nous montrons enfin que la capacité de Viterbo d’une sous-variété lagrangienne compacte n’est jamais nulle.
The aim of this paper is to compare two symplectic capacities in related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold is nonzero.
@article{BSMF_2004__132_4_509_0,
author = {Hermann, David},
title = {Inner and outer hamiltonian capacities},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
volume = {132},
year = {2004},
pages = {509-541},
doi = {10.24033/bsmf.2472},
mrnumber = {2131902},
zbl = {1083.53083},
language = {en},
url = {http://dml.mathdoc.fr/item/BSMF_2004__132_4_509_0}
}
Hermann, David. Inner and outer hamiltonian capacities. Bulletin de la Société Mathématique de France, Tome 132 (2004) pp. 509-541. doi : 10.24033/bsmf.2472. http://gdmltest.u-ga.fr/item/BSMF_2004__132_4_509_0/
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