Advertisement

Fixed point results for symplectic maps related to the arnold - conjecture

  • A. Floer
  • E. Zehnder
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1125)

Keywords

Periodic Solution Fixed Point Theorem Symplectic Manifold Symplectic Structure Fixed Point Theory 
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]
    Arnold, V.I.: Mathematical methods of classical mechanics. (Appendix 9) Berlin-Heidelberg New York: Springer 1978.CrossRefzbMATHGoogle Scholar
  2. [2]
    Arnold, V.I.: Proceedings of symposia in pure mathematics. Vol. XXVIII AMS, p.66, 1976.Google Scholar
  3. [3]
    Banyagá, A.: Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique. Comment. Math. Helvetici 53 (1978), 174–227.CrossRefzbMATHGoogle Scholar
  4. [4]
    H. Beresticki, J.-M. Lasry, G. Mancini, B. Ruf: Existence of Multiple Periodic Orbits on Star-Shaped Hamiltonian Surfaces”, to appear 1984.Google Scholar
  5. [5]
    Birkhoff, G.D.: Proof of Poincaré's Geometric Theorem. Trans.Amer.Math.Soc. 14, (1913), 14–22.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Birkhoff, G.D.: An Extension of Poincaré's Last Geoemtric theorem. Acta Math. 47 (1925)Google Scholar
  7. [7]
    Chaperon, M.: Quelques Questions de Géométrie symplectique. Séminaire Bourbaki 1982/83, n° 610, to appear in Astérisque.Google Scholar
  8. [8]
    M. Chaperon, E. Zehnder: Quelques résultats globaux en géométrie symplectique. In: Géométrie symplectique et de contact: antour du théorème de Poincaré — Birkhoff, Hermann, Paris 1984, 51–122.Google Scholar
  9. [9]
    Conley, C., Zehnder, E.: The Birkhoff-Lewis Fixed point theorem and a Conjecture of V.I. Arnold, Invent. math. 73 (1983), 33–49.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Conley, C., Zehnder, E.: Subharmonic solutions and Morse-theory”, Physica 124A (1984), 649–658.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Conley, C.: Isolated invariant sets and the Morse-index. CBMS, Regional Conf. Series in Math. Vol. 38 (1978).Google Scholar
  12. [12]
    A. Floer: Proof of the conjecture for surfaces and generalizations for certain Kähler manifolds. PhD-Thesis RUB, Bochum 1984.Google Scholar
  13. [13]
    B. Fortune, A. Weinstein: A symplectic fixed point theorem for complex projective spaces. Preprint, Berkeley 1984.Google Scholar
  14. [14]
    B. Fortune, PhD. thesis, Univ. of Cal., Berkeley, 1984.Google Scholar
  15. [15]
    J. Marsden, A. Weinstein: Reduction of symplectic manifolds with symmetry, Reports on Math. Phys. 5(1974), 121–130.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Moser, J.: On the volume elements on a manifold. Transactions Amer. Math. Soc. 120 (1965), 286–294.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Moser, J.: A fixed point theorem in symplectic geometry. Acta Math. 141 (1978), 17–34.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Nikishin, N. Fixed points of diffeomorphisms on the twosphere that preserve area. Funkcional Anal. i Prelozen 8 (1974), 84–85.CrossRefGoogle Scholar
  19. [19]
    Poincaré, H.: Sur un théorème de Géométrie. Rend. Circolo Mat. Palermo 33 (1912), 375–407.CrossRefGoogle Scholar
  20. [20]
    H. Poincaré: "Les méthodes nouvelles de la mécanique célèste", Gauthiers Villars Paris 1899, tome III, p. 214.Google Scholar
  21. [21]
    Rabinowitz, P.: Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 31 (1978), 157–184.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Salamon, D.: Connected simple systems and the Conley Index of Isolated invariant sets. MRC Technical summary Report 2753, 1984, Madison.Google Scholar
  23. [23]
    J. Sikorav: Points fixes d'une symplectomorphisme homologue à l'identité. To appear in C.R. Acad. Sc. Paris, 1984.Google Scholar
  24. [24]
    J. Sikorav: Points fixed d'une application symplectique homologue à l'identité. PhD Thesis Université de Paris-Sud, 1984.Google Scholar
  25. [25]
    Simon, C.P.: A bound for the Fixed point Index of an Areapreserving map with Applications to Mechanics. Invent. math. 26 (1974), 187–200.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Weinstein, A.: C° perturbation theorems for symplectic fixed points and Lagrangian intersections. Lecture Notes of the AMS summer Institute on nonlinear Functional Analysis and Applications, Berkeley 1983.Google Scholar
  27. [27]
    Weinstein, A.: Lectures on symplectic manifolds. CBMS Regional Conference series in math. Vol. 29 (1977).Google Scholar
  28. [28]
    E. Zehnder: Periodic solutions of Hamiltonian equations. Springer Lecture Notes in Math. 1031 (1983), 172–213.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Birkhoff, G.D.: The restricted problem of three bodies. Rend. Circolo Mat. Palermo 39 (1915), 265–334.CrossRefzbMATHGoogle Scholar
  30. [30]
    C. Conley and E. Zehnder: Morse-type Index theory for Flows and Periodic Solutions for Hamiltonian equations. Comm. on Pure and Appl. Math. Vol. XXXVII (1984), 207–253.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • A. Floer
    • 1
  • E. Zehnder
    • 1
  1. 1.Mathematisches Institut derRuhr-Universität BochumBochumGermany

Personalised recommendations