Symplectic topology and Hamiltonian dynamics
@article{Ekeland1988SymplecticTA, title={Symplectic topology and Hamiltonian dynamics}, author={Ivar Ekeland and Helmut H. Hofer}, journal={Mathematische Zeitschrift}, year={1988}, volume={200}, pages={355-378} }
On etudie des applications symplectiques non lineaires. Capacites symplectiques. Construction d'une capacite symplectique. Problemes de plongement. Problemes de rigidite
244 Citations
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Soit P une variete symplectique compacte et soit L⊂P une sous-variete lagrangienne avec π 2 (P,L)=0. Pour un diffeomorphisme exact φ de P avec la propriete que φ(L) coupe L transversalement, on…
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The starting point of this investigations is the following. Let H: R 2n →R be a smooth function, and consider the Hamiltonian system: (E 0 ) −Jx=H'(x). Here J=*=−J −1 defines the symplectic structure…
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On considere un champ vectoriel hamiltonien x˙=J⊇H(x)=:X H (x) sur x∈R 2n , H etant une fonction lisse dont le gradient ⊇H est defini par rapport a la metrique euclidienne. On cherche des solutions…
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SummaryIn this paper we construct symplectic forms
$$\tilde \omega _k , k \geqq 0$$
, on a compact manifold
$${\tilde Y}$$
which have the same homotopy theoretic invariants, but which are not…
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In this paper we introduce symplectic invariants for convex Hamiltonian energy surfaces and their periodic trajectories and show that these quentities satisfy several nontrivial relations. In…
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1. A Survey of Basic Problems and Results.- 2. Methods to Prove the h-Principle.- 3. Isometric C?-Immersions.- References.- Author Index.
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© Société mathématique de France, 1987, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les…