Abstract
Recently I have developed an algorithm of the local analysis of singularities. It is equally applied in the systems of algebraic equations and in the systems of ordinary equations and in the partial differential equations [1,2]. Here I shall show its effectivity by two examples of Hamiltonian systems. Indeed I prefer to study properties of arbitrary systems and to apply them to the Hamiltonian systems [3].
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References
A. D. Bruno and A. Soleev, First approximations of algebraic equations, Doklady Akad. Nauk, 230 (to appear), in Russian. Soviet Mathematics Doklady in English.
A. D. Bruno, First approximations of differential equations, Ibid.
A. D. Bruno, 1990, A local analysis of Hamiltonian systems, Preprint I.H.E.S./M/1990/33.
A. D. Bruno, 1990, The Restricted Three Body Problem, Nauka, Moscow (in Russsian). English translation: Walter de Gruyter, Berlin, 1993.
M. Hénon, 1968, Sur les orbites interplanétaires qui rencontrent deux fois la terre, Bull. Astron., Ser. 3, t. 3:3, pp. 377-402.
A. D. Bruno, 1978, On periodic flybys of the moon, Preprint No. 91 of Inst. Applied Math., Moscow (in Russian). English version: Celest. Mech, 1981, 24, pp. 255-268.
A. D. Bruno, 1992, General approach to a study of complicated bifurcations, Prikladnaya Mekhanika, 28:12, pp. 83-86 (in Russian). English translation in Soviet Applied Mathematics.
A. D. Bruno, 1993, Multiple periodic solutions of the restricted three-body problem in the Sun-Jupiter case, Preprint of Inst. Applied Math., Moscow (in Russian), to appear.
A. D. Bruno, 1979, Local Metchods in Nonlinear Differential Equations, Nauka, Moscow (in Russian). English translation: Springer-Verlag, Berlin etc., 1989.
A. D. Bruno and V. Yu. Petrovitch, Regularization of oscillations of a satellite on a very stretched orbit, 1993, Preprint of Inst. Appl. Math., Moscow (in Russian), to appear.
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Bruno, A.D. (1994). Singular Perturbation in Hamiltonian Mechanics. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_4
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DOI: https://doi.org/10.1007/978-1-4899-0964-0_4
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