Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-30T23:57:14.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Symplectic displacement energy for Lagrangian submanifolds

Published online by Cambridge University Press:  19 September 2008

Leonid Polterovich
Leonid Polterovich
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently H. Hofer defined a new symplectic invariant which has a beautiful dynamical meaning. In the present paper we study this invariant for Lagrangian submanifolds of symplectic manifolds. Our approach is based on Gromov's theory of pseudo-holomorphic curves.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 357 - 367
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Arnold, V.I. and Givental, A.B.. Symplectic geometry. Dynamical Systems 4, Encyclopedia of Math. Sciences. Springer, Berlin, 1990.Google Scholar
[2]Eliashberg, Ya. & Hofer, H.. Towards the definition of symplectic boundary. Preprint. 1991.Google Scholar
[3]Gromov, M.. Pseudo-holomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), 307–347.CrossRefGoogle Scholar
[4]Hofer, H.. On the topological properties of symplectic maps. Proc. Royal Society of Edinburgh 115A (1990), 25–38.CrossRefGoogle Scholar
[5]Hofer, H.. Estimates for the energy of a symplectic map. Preprint. 1991.Google Scholar
[6]Lalonde, F.. Engouffrement hamiltonien de sous-variétés lagrangiennes irrationnelles avec petit nombre de Betti. Preprint, 1991.Google Scholar
[7]Polterovich, L.. Transversal Hamiltonian fields and differential relations. Preprint, 1991.Google Scholar
[8]Sikorav, J-C.. Quelques propriétés des plongements Lagrangiens. Preprint. 1990.Google Scholar
[9]Sikorav, J.-C.. Systémes Hamiltoniens et Topologie Symplectique. ETS Editrice, Pisa, 1990.Google Scholar