Mathematische Zeitschrift

, Volume 216, Issue 1, pp 417–430 | Cite as

On quadratic symplectic mappings

  • Jürgen Moser


Algebraic Number Symplectic Mapping Shear Transformation Jacobian Conjecture Birkhoff Normal Form 
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  1. 1.
    Baker, A.: Effective methods in the theory of numbers. In: Actes du Congrès International des Mathématiciens 1970, vol. 1, pp. 19–26, Paris: Gauthier-Villars 1971 (see p. 22)Google Scholar
  2. 2.
    Baker, A.: Transcendental Number Theory. Cambridge: Cambridge University Press 1975zbMATHGoogle Scholar
  3. 3.
    Bass, H., Cornell, E.H., Wright, D.: The Jacobian Conjecture: reduction of degree and formal expansion of the inverse. Bull. Am. Math. Soc.7, 287–330 (1982)zbMATHCrossRefGoogle Scholar
  4. 4.
    Feldman, N.I.: Estimate for a linear form of logarithms of algebraic numbers. Mat. Sb.76 (118), 304–309 (1968)MathSciNetGoogle Scholar
  5. 5.
    Feldman, N.I.: An improvement of the estimate for a linear form in the logarithms of algebraic numbers. Mat. Sb.77 (119), 423–436 (1968)MathSciNetGoogle Scholar
  6. 6.
    Friedland, S., Milnor, J.: Dynamical properties of plane polynomial automorphisms. Ergod. Theory Dyn. Syst.9, 67–99 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Hénon, M.: Numerical study of quadratic area-preserving mappings. Q. Appl. Math.27, 291–312 (1969)zbMATHGoogle Scholar
  8. 8.
    Hénon, M.: A two dimensional mapping with a strange attractor. Commun. Math. Phys.50, 69–77 (1976)zbMATHCrossRefGoogle Scholar
  9. 9.
    Hénon, M., Heiles, C.: The applicability of the third integral of motion; some numerical experiments. Astron. J.69, 73–79 (1964)CrossRefGoogle Scholar
  10. 10.
    Lazutkin, V.F.: Splitting of complex separatrices. Funkt. Anal. Appl.22, 154–156 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Moser, J.: On the integrability of area-preserving Cremona mappings near an elliptic point. Bol. Soc. Mat. Mex. 176–180 (1960)Google Scholar
  12. 12.
    Rüssmann, H.: Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Math. Ann.169, 55–72 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Siegel, C.L., Moser, J.K.: Lectures on Celestial Mechanics. Berlin Heidelberg New York: Springer 1971zbMATHGoogle Scholar
  14. 14.
    Simó, C.: Stability of degenerate fixed points of analytic area-preserving mappings. Astérisque98–99, 184–194 (1982)Google Scholar
  15. 15.
    Wang, S.: A Jacobian criterion for separability. J. Algebra65, 453–494 (1980)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jürgen Moser
    • 1
  1. 1.Eidgenössische Technische HochschuleETH ZürichZürichSwitzerland

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