This work was partly prepared during the authors visit to the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, April–May, 1981.
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References
J. MOSER: On Invariant Curves of Area-Preserving Mappings of an Annulus. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. IIa, Nr. 1 (1962) 1–20.
J. MOSER: A Rapidly Convergent Iteration Method and Nonlinear Differential Equations II. Ann.Scuola Norm. Sup. Pisa (1966) 499–535.
H. ROSSMANN: Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II, Nr. 5 (1970) 67–105.
J. MOSER: MR 42 # 8037.
J. MOSER: Stable and Random Motions in Dynamical Systems. Princeton University Press. Princeton, N.J. (1973).
M.R. HERMAN: Demonstration du théorème des courbes translatées de nombre de rotation de type constant. Manuscript 1981.
A.N. KOLMOGOROV: On Quasi Periodic Motions Under Small Perturbations of the Hamiltonian. Doklady Akad. Nauk. SSSR 98 (1954) Nr. 4 527–530.
V.I. ARNOLD: Small Denominators I. On the Mapping of a Circle into Itself. Izv. Akad. Nauk. SSSR Ser. Math. 25 Nr. 1 (1961) 21–86
Am. Mat. Soc. Transl., Ser. 2, 46, 213–284.
. Usp. Mat. Nauk. SSSR 18 (1963) 13–40
Russian Math. Surveys 18, 9–36.
V.I. ARNOLD: Small Divisor Problems in Classical and Celestial Mechanics Usp. Mat. Nauk. SSSR 18 (1963) 91–192.
Russian Math. Surveys 18, 85–191.
J. MOSER: Convergent Series Expansions for Quasi-Periodic Motions. Math. Ann. 169 (1967) 136–176.
J.M. GREENE: The Calculation of KAM Surfaces. Annals New York Acad. Sci. 357 (1980) 80–89.
H. JACOBOWITZ: Implicit Function Theorem and Isometric Embeddings. Ann. of Math. 95 (1972) 191–225.
E. ZEHNDER: Generalized Implicit Function Theorems with Applications to Some Small Divisor Problems, I. Comm. Pure Appl. Math. 28 (1975) 91–140.
G.G. LORENTZ: Approximation of Functions. Athena Series 1966. Holt, Rinehart and Winston, Inc.
K.I. BABENKO: On the Best Approximation of a Class of Analytic Functions. Izv. 22 (1958) 631–640.
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Rüssmann, H. (1983). On the existence of invariant curves of twist mappings of an annulus. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061441
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DOI: https://doi.org/10.1007/BFb0061441
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