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Mathematische Annalen

, Volume 219, Issue 2, pp 105–121 | Cite as

Moser's implicit function theorem in the framework of analytic smoothing

  • Eduard Zehnder
Article

Keywords

Implicit Function Theorem Analytic Smoothing 
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References

  1. 1.
    Jacobowitz, H.: Implicit function theorems and isometric embeddings. Annals of Math. 191–225 (1972)Google Scholar
  2. 2.
    Nirenberg, L.: An abstract form of the nonlinear Cauchy-Kowalewski theorem. Jour. Differential Geometry6, 561–576 (1972)Google Scholar
  3. 3.
    Schwartz, J.: On Nash's implicit function theorem. Comm. Pure Appl. Math.13, 509–530 (1960)Google Scholar
  4. 4.
    Sergeraert, F.: Un théorème the fonctions implicites sur certains espaces de Fréchet et Quelques applications. Ann. Sci. École Norm. Sup., 4e Serie5, 599–660 (1972)Google Scholar
  5. 5.
    Hamilton, R.: The inverse function theorem of Nash and Moser (preprint Cornell University 1974)Google Scholar
  6. 6.
    Nash, J.: The embedding problem for Riemann manifolds. Ann. of Math.63, 20–63 (1956)Google Scholar
  7. 7.
    Moser, J.: On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss., Göttingen, Math. Phys. Kl. II, 1–20 (1962)Google Scholar
  8. 8.
    Moser, J.: A new technique for the construction of solutions of nonlinear differential equations. Proc. Nat. Acad. Sciences47, 1824–1831 (1961).Google Scholar
  9. 9.
    Moser, J.: A rapidly convergent iteration method and nonlinear partial differential equations I and II. Ann. Scuola Norm. Sup. Pisa20, 265–315, 499–535 (1966)Google Scholar
  10. 10.
    Arnold, V.: Proof of a theorem of A. N. Kolmogorov on the invariance of quasiperiodic motions under small perturbations of the Hamiltonian. Russian Math. Surveys18, 9–36 (1963)Google Scholar
  11. 11.
    Arnold, V.: Small denominators and problems of stability of motions in classical and celestial mechanics. Surveys18, 85–193 (1963)Google Scholar
  12. 12.
    Zehnder, E.: Generalized implicit function theorems with applications to some small divisor problems, I. Comm. Pure Appl. Math.28, 91–140 (1975)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Eduard Zehnder
    • 1
  1. 1.Mathematisches Institut der Universität Erlangen-NürnbergErlangenFederal Republic of Germany

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