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On the numerical treatment of a small divisor problem. (English) Zbl 0497.65047

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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[2] Arnol’d V.I.: Small denominators and problems of stability of motions in classical and celestial mechanics. Russian Math. Surveys18, 85-193 (1963) · Zbl 0135.42701 · doi:10.1070/RM1963v018n06ABEH001143
[3] Gutknecht, M.H.: Existence of a solution to the discrete Theodorsen equation for conformal mappings. Math. Comput.31, 478-480 (1977) · Zbl 0365.30004 · doi:10.1090/S0025-5718-1977-0440021-1
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[6] Moser, J.: On invariant curves of area preserving mappings of an annulus. Nachr. Akad. Wiss. G?ttingen, Math. Phys. Kl. II, 1-20 (1962) · Zbl 0107.29301
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[8] Moser, J.: Stable and random motions in dynamical systems. Princeton University Press 1973 · Zbl 0271.70009
[9] R?ssmann, H.: Kleine Nenner II: Bemerkungen zur Newton’schen Methode. Nachr. Akad. Wiss. G?ttingen Math.-Phys. Kl. 1-10 (1972)
[10] R?ssmann, H.: Konvergente Reihenentwicklung in der St?rungstheorie der Himmelsmechanik. Selecta Mathematica V, 93-257, Springer 1979
[11] Zehnder, E.: Generalized implicit functions theorems with applications to some small divisor problems I and II. Comm. Pure Appl. Math.28, 91-140 (1975) and29, 49-111 (1976) · Zbl 0309.58006 · doi:10.1002/cpa.3160280104
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