Abstract
The aim of this note is to show that two of Arnol’d’s celebrated conjectures in symplectic geometry can be proven without any knowledge of functional analysis. For the convenience of the reader, we shall not use the language of differential geometry before the conclusion, where the advantages of our method are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. C. Conley and E. Zehnder, ‘The Birkhoff-Lewis theorem and a conjecture of V. I. Arnol’d’, Inv. Math, 73 (1983), 33–49.
M. Chaperon, ‘Quelques questions de géométrie symplectique’, Séminaire Bourbaki, 1982–83, Astérisque 105–106 (1983)
M. Chaperon, ‘Quelques questions de géométrie symplectique’, Séminaire Bourbaki, 1982–83, Astérisque 105–106 (1983), 231–249.
M. Chaperon and E. Zehnder, ‘Quelques résultats globaux en géométrie symplectique’, Géométrie symplectique et de contact: autour du théorème de Poincaré-Birkhoff, Travaux en cours, Hermann, Paris (1984), 51–121.
H. Hofer, ‘Lagrangian embeddings and critical point theory’, Ann. Inst. Henri Poincaré, Analyse non linéaire, 2 (1985), 407–462.
F. Laudenbach and J. C. Sikorav, ‘Persistance d’intersection avec-la section nulle…’, Invent. Math. 82 (1985), 349–357.
J. C. Sikorav, ‘Problèmes d’intersections et de points fixes en géométrie Hamiltonienne’, preprint, Orsay (1985).
M. Chaperon, ‘Generating phase functions and Hamiltonian systems’, preprint, Ecole Polytechnique (1986).
H. Hofer and E. Zehnder, ‘Periodic solutions on hypersurfaces and a result by C. Viterbo’, to appear in Inventiones Math.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company
About this chapter
Cite this chapter
Chaperon, M. (1987). An Old-Fashioned Method in the Calculus of Variations. In: Rabinowitz, P.H., Ambrosetti, A., Ekeland, I., Zehnder, E.J. (eds) Periodic Solutions of Hamiltonian Systems and Related Topics. NATO ASI Series, vol 209. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3933-2_7
Download citation
DOI: https://doi.org/10.1007/978-94-009-3933-2_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8245-7
Online ISBN: 978-94-009-3933-2
eBook Packages: Springer Book Archive