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Bulletin of the American Mathematical Society

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An implicit function theorem for small divisor problems

Author: E. Zehnder
Journal: Bull. Amer. Math. Soc. 80 (1974), 174-179
MSC (1970): Primary 35A35, 58C15, 70F15, 70H20
MathSciNet review: 0339259
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  • 1. John Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20–63. MR 0075639
  • 2. A. N. Kolmogorov, Théorie générale des systèmes dynamiques et mécanique classique, Proceedings of the International Congress of Mathematicians, Amsterdam, 1954, Vol. 1, Erven P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam, 1957, pp. 315–333 (French). MR 0097598
  • 3. V. I. Arnol′d, Small denominators and problems of stability of motion in classical and celestial mechanics, Uspehi Mat. Nauk 18 (1963), no. 6 (114), 91–192 (Russian). MR 0170705
  • 4. J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1962 (1962), 1–20. MR 0147741
  • 5. Jürgen Moser, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1824–1831. MR 0132859
  • 6. J. Moser, A rapidly convergent iteration method and non-linear partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), I: pp, 265-315, II: pp. 499-535. MR 33 #7667; 34 #6280.
  • 7. J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. MR 0433481
  • 8. Francis Sergeraert, Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications, Ann. Sci. École Norm. Sup. (4) 5 (1972), 599–660 (French). MR 0418140
  • 9. Howard Jacobowitz, Implicit function theorems and isometric embeddings, Ann. of Math. (2) 95 (1972), 191–225. MR 0307127
  • 10. L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561–576. Collection of articles dedicated to S. S. Chern and D. C. Spencer on their sixtieth birthdays. MR 0322321
  • 11. Helmut Rüssmann, Kleine Nenner. II. Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1972), 1–10 (German). MR 0309297
  • 12. Jürgen Moser, Stable and random motions in dynamical systems, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1973. With special emphasis on celestial mechanics; Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N. J; Annals of Mathematics Studies, No. 77. MR 0442980
  • 13. S. Graff, On the conservation of hyperbolic invariant tori for Hamiltonian systems, Dissertation, New York University, New York, June, 1971.
  • 14. S. Sternberg, Celestial mechanics, Part II, Benjamin, New York, 1969.
  • 15. E. Zehnder, The Moser-Nash implicit function theorem for small divisor problems (to appear).

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