Acta Mathematica

, Volume 150, Issue 1, pp 255–296 | Cite as

Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations

  • Jürgen K. Moser
  • Sidney M. Webster
Article

Keywords

Normal Form Formal Power Series Real Surface Real Hypersurface Hyperbolic Surface 

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References

  1. [1]
    Bedford, E. & Gaveau, B., Envelopes of holomorphy of certain 2-spheres in C2. To appear inAmer. J. Math., 105 (1983).Google Scholar
  2. [2]
    Birkhoff, G. D., The restricted problem of three bodies.Rend. Circ. Mat. Palermo, 39 (1915), 265–334. (In particular p. 310 and p. 329.)MATHCrossRefGoogle Scholar
  3. [3]
    —, Surface transformations and their dynamical applications.Acta Math., 43 (1920), 1–119. (In particular p. 7.)MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Bishop, E., Differentiable manifolds in complex Euclidean space.Duke Math. J., 32 (1965), 1–22.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Chern, S. S. &Moser, J. K., Real hypersurfaces in complex manifolds.Acta Math., 133 (1974), 219–271.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Freeman, M., Polynomial hull of a thin two-manifold.Pacific J. Math., 38 (1971), 377–389.MATHMathSciNetGoogle Scholar
  7. [7]
    Hunt, L. R., The local envelope of holomorphy of ann-manifold inC n.Bol. Un. Mat. Ital., 4 (1971), 12–35.MATHGoogle Scholar
  8. [8]
    Kenig, C. &Webster, S., The local hull of holomorphy of a surface in the space of two complex variables.Invent. Math., 67 (1982), 1–21.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Lewy, H., On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables.Ann. of Math., 64 (1956), 514–522.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Moser, J., On the integrability of area-preserving Cremona mappings near an elliptic fixed point.Boletin de la Sociedad Matematica Mexicana (2) 5 (1960), 176–180.Google Scholar
  11. [11]
    Siegel, C. L. & Moser, J. K.,Lectures on Celestial Mechanics. Springer, 1971. (In particular, p. 166ff.)Google Scholar
  12. [12]
    Siegel, C. L., Vereinfachter Beweis eines Satzes von J. Moser.Comm. Pure Appl. Math., 10 (1957), 305–309.MATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1983

Authors and Affiliations

  • Jürgen K. Moser
    • 1
  • Sidney M. Webster
    • 2
  1. 1.Forschungsinstitut für Mathematik ETHZürichSwitzerland
  2. 2.University of MinnesotaUSA

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