Skip to main content

An elementary proof of the conley — Zehnder theorem in symplectic geometry

Part of the Lecture Notes in Mathematics book series (LNM,volume 1125)

Keywords

  • Canonical Projection
  • SYMPLECTIC Geometry
  • Lift Property
  • Reactionary Opinion
  • Hermitian Product

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V.I. ARNOLD, Sur une propriété topologique des applications globalement canoniques de la mécanique classique, C.R. Acad. Sc. Paris, t. 261 (Nov. 1965), Group 1, 3719–3722.

    MATH  Google Scholar 

  2. V.I. ARNOLD, Méthodes mathématiques de la mécanique classique, Mir, Moscou, 1976.

    Google Scholar 

  3. R. BOTT, Lectures on Morse theory, old and new, Bull. (new series) of the AMS, Vol. 7, no 2 (sept. 1982), 331–358.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M. CHAPERON, E. ZEHNDER, Quelques résultats globaux en géométrie symplectique, Séminaire sud-rhodanien de géométrie III: autour du théorème de Poincaré-Birkhoff, Travaux en cours, Hermann, Paris (1984), 51–121.

    Google Scholar 

  5. M. CHAPERON, Quelques questions de géométrie symplectique [d'après, entre autres, Poincaré, Arnold, Conley et Zehnder], Séminaire Bourbaki 1982–83, Astérisque 105–106 (1983), 231–249.

    MathSciNet  MATH  Google Scholar 

  6. M. CHAPERON, Une idée du type "géodésiques brisées" pour les système hamiltoniens, C.R. Acad. Sc. Paris, t. 298, no 13 (1984), 293–296.

    MathSciNet  MATH  Google Scholar 

  7. M. CHAPERON, Questions de géométrie symplectique, Séminaire Sud-Rhodanien IV, Balaruc (may 1984), to appear in Travaux en cours, Hermann, Paris.

    Google Scholar 

  8. C.C. CONLEY, E. ZEHNDER, The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Inv. Math. 73 (1983), 33–49.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. J. MILNOR, Morse theory, Annals of Math. Study 51, Princeton, 1963.

    Google Scholar 

  10. F. LAUDENBACH, J.C. SIKORAV, Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent, preprint, Université Paris-Sud, 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Chaperon, M. (1985). An elementary proof of the conley — Zehnder theorem in symplectic geometry. In: Braaksma, B.L.J., Broer, H.W., Takens, F. (eds) Dynamical Systems and Bifurcations. Lecture Notes in Mathematics, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075631

Download citation

  • DOI: https://doi.org/10.1007/BFb0075631

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15233-0

  • Online ISBN: 978-3-540-39411-2

  • eBook Packages: Springer Book Archive