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References
Andronov, A. A., Vitt, A. A. and Khaikin, S. E.: 1966,Theory of Osciilators, Addison-Wesley.
Deprit, A.: 1969, ‘Canonical transformations depending on a small parameter’,Celest. Mech. 1, 12–30.
Depril, A.: 1981, ‘The Elimination of the Parallax in Satellite Theory’,Celest. Mech. 24, 111–153.
Deprit, A.: 1982, ‘The ideal resonance problem at first order’,Advances in the Astronomical Sciences 46, 521–526.
Deprit, A. and Richardson, D.: 1985, ‘Disemcumbering transformations for ideal resonance problem’. Unpublished.
Ferraz-Mello, S.: ‘Resonance in regular variables I: Morphogenetic analysis of the orbits in the case of first order resonance’,Celes. Mech. 35, 209–220.
Ferraz-Mello, S.: 1985b, ‘Resonance in regular variables II: formal solutions for central and non-central first order resonance’,Celes. Mech. 35, 221–234.
Garfinkel, B.: 1966, ‘Formal solution in the problem of small divisors’,Astron. J. 71, 657–669.
Garfinkel, B.: 1972a, ‘Regularization in the ideal resonance problem’,Celest. Mech. 5, 189–203.
Garfinkel, B.: 1972b, ‘Normality condition in the ideal resonance problem’,Celest. Mech. 6, 151–166.
Garfinkel, B.: 1976, ‘A theory of libration’,Celest. Mech. 13, 229–246.
Garfinkel, B.: 1982, ‘On resonance in Celestial Mechanics’,Celest. Mech. 28, 275–290.
Garfinkel, B., Jupp, A. H. and Williams, C. A.: 1971, ‘A recursive von Zeipel algorithm for the ideal resonance problem’,Astron. J. 76, 157–160.
Garfinkel, B. and Williams, C. A.: 1974, ‘A second-order global solution of the ideal resonance problem’,Celest. Mech. 9, 105–125.
Henrard, J.: 1970, ‘On a perturbation theory using Lie transforms’,Celest. Mech. 3, 107–120.
Henrard, J. and Lemaître, A.: 1983, ‘A second fundamental model for resonance’,Celest. Mech. 30, 197–218.
Henrard, J. and Lemaître, A.: 1987, ‘A perturbation method for problem with two critical arguments’,Celest. Mech. 39, 213–238.
Howland, R. A.: 1988a, ‘A new approach to the librational solution in the ideal resonance problem’,Celest. Mech., this issue, pp. 209–226.
Howland, R. A.: 1988b, ‘A note on the application of a generalized canonical approach to non-linear Hamiltonian system’,Celest. Mech., in print.
Huilgol, R. R.: 1978, ‘Hopf-Friedricks Bifurcation and the Hunting of a Railway Axle’,Quarterly Appl. Math. 36, 85–94.
Jupp, A. H.: 1969, ‘The Ideal Resonance Problem’,Astron. J. 74, 35.
Jupp, A. H.: 1972, ‘A second-order solution of the Ideal Resonance Problem by Lie series’,Celest. Mech. 5, 8–26.
Jupp, A. H.: 1974, ‘The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions’,Celest. Mech. 8, 523–530.
Jupp, A. H.: 1982, ‘A comparison of the Bohlin-Von Zeipel and Bohlin-Lie series methods in resonant systems’,Celest. Mech.,26, 413–422.
Jupp, A. H. and Abdulla, A. Y.: 1984, ‘The Ideal Resonance Problem: A comparison of two formal solutions I,Celest. Mech. 34, 411–423.
Jupp, A. H. and Abdulla, A. Y.: 1985, ‘The Ideal Resonance Problem: A comparison of two formal solutions II’,Celest. Mech. 37, 183–197.
Kamel, A. A.: 1970, ‘Perturbation method in the theory on nonlinear oscillations’,Celest. Mech. 3, 90–106.
Minorsky, N.: 1962,Nonlinear Oscillations, Van Nostrand Co.
Poincaré, H.: 1983, ‘Les méthodes nouvelles de la Mécanique Céleste. Vol. 2, Paris Gauthier-Villars.
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Henrard, J., Wauthier, P. A geometric approach to the Ideal Resonance Problem. Celestial Mechanics 44, 227–238 (1988). https://doi.org/10.1007/BF01235537
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DOI: https://doi.org/10.1007/BF01235537