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}
}
  • I. Ekeland, H. Hofer
  • Published 1 September 1989
  • Physics, Mathematics
  • Mathematische Zeitschrift
On etudie des applications symplectiques non lineaires. Capacites symplectiques. Construction d'une capacite symplectique. Problemes de plongement. Problemes de rigidite 
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244 Citations
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244 Citations

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References

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Two symplectic fixed-point theorems with applications to Hamiltonian dynamics
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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