Advertisement

Inventiones mathematicae

, Volume 73, Issue 1, pp 33–49 | Cite as

The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold

  • C. C. Conley
  • E. Zehnder
Article

Keywords

Point Theorem Fixed Point Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amann, H., Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Annali Sc. Norm. Sup. Pisa, Serie IV. Vol.7, 539–603 (1980)Google Scholar
  2. 2.
    Arnold, V.I.: Mathematical methods of classical mechanics. (Appendix 9). Berlin-Heidelberg-New York: Springer 1978Google Scholar
  3. 3.
    Arnold, V.I.: Proceedings of symposia in pure mathematics. Vol. XXVIII A.M.S., p. 66, 1976Google Scholar
  4. 4.
    Banyaga, A.: Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique. Comment. Math. Helvetici53, 174–227 (1978)Google Scholar
  5. 5.
    Banyaga, A.: On fixed points of symplectic maps. PreprintGoogle Scholar
  6. 6.
    Conley, C.C.: Isolated invariant sets and the Morse index. CBMS, Regional Conf. Series in Math., vol. 38 (1978)Google Scholar
  7. 7.
    Conley, C.C., Zehnder, E.: Morse type index theory for flows and periodic solutions for Hamiltonian equations. To appear in Comm. Pure and Appl. Math.Google Scholar
  8. 8.
    Moser, J.: A fixed point theorem in symplectic geometry. Acta Math.141, 17–34 (1978)Google Scholar
  9. 9.
    Moser, J.: Proof of a generalized form of a fixed point theorem due to G.D. Birkooff. Lecture Notes in Mathematics, Vol. 597: Geometry and Topology, pp. 464–494. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  10. 10.
    Moser, J.: On the volume elements on a manifold. Transactions Amer. Math. Soc.120, 286–294 (1965)Google Scholar
  11. 11.
    Poincaré, H.: Méthodes nouvelles de la mécanique célèste. Vol. 3, chap. 28. Paris: Gauthier Villars 1899Google Scholar
  12. 12.
    Weinstein, A.: Lectures on symplectic manifolds. CBMS, Regional conf. series in Math., vol. 29 (1977)Google Scholar
  13. 13.
    Earle, C.J., Eells, J.: A fibre bundle description of Teichmüller theory. J. Diff. Geometry3, 19–43 (1969)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • C. C. Conley
    • 1
  • E. Zehnder
    • 2
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Abteilung MathematikRuhr-Universität, BochumBochumFederal Republic of Germany

Personalised recommendations