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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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An implicit function theorem for small divisor problems
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by E. Zehnder PDF
Bull. Amer. Math. Soc. 80 (1974), 174-179
References
  • John Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20–63. MR 75639, DOI 10.2307/1969989
  • 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
  • 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
  • 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 147741
  • 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 132859, DOI 10.1073/pnas.47.11.1824
  • 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.
  • J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, 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. MR 0433481
  • 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 418140, DOI 10.24033/asens.1239
  • Howard Jacobowitz, Implicit function theorems and isometric embeddings, Ann. of Math. (2) 95 (1972), 191–225. MR 307127, DOI 10.2307/1970796
  • L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561–576. MR 322321, DOI 10.4310/jdg/1214430643
  • Helmut Rüssmann, Kleine Nenner. II. Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1972), 1–10 (German). MR 309297
  • Jürgen Moser, Stable and random motions in dynamical systems, Annals of Mathematics Studies, No. 77, 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. 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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Additional Information
  • Journal: Bull. Amer. Math. Soc. 80 (1974), 174-179
  • MSC (1970): Primary 35A35, 58C15, 70F15, 70H20
  • DOI: https://doi.org/10.1090/S0002-9904-1974-13407-5
  • MathSciNet review: 0339259