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Singular Perturbation in Hamiltonian Mechanics

  • A. D. Bruno
Part of the NATO ASI Series book series (NSSB, volume 331)

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].

Keywords

Periodic Solution Hamiltonian System Singular Perturbation Hamiltonian Function Restricted Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. D. Bruno and A. Soleev, First approximations of algebraic equations, Doklady Akad. Nauk, 230 (to appear), in Russian. Soviet Mathematics Doklady in English.Google Scholar
  2. 2.
    A. D. Bruno, First approximations of differential equations, Ibid.Google Scholar
  3. 3.
    A. D. Bruno, 1990, A local analysis of Hamiltonian systems, Preprint I.H.E.S./M/1990/33.Google Scholar
  4. 4.
    A. D. Bruno, 1990, The Restricted Three Body Problem, Nauka, Moscow (in Russsian). English translation: Walter de Gruyter, Berlin, 1993.Google Scholar
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    M. Hénon, 1968, Sur les orbites interplanétaires qui rencontrent deux fois la terre, Bull. Astron., Ser. 3, t. 3:3, pp. 377-402.Google Scholar
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    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.Google Scholar
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  8. 8.
    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.Google Scholar
  9. 9.
    A. D. Bruno, 1979, Local Metchods in Nonlinear Differential Equations, Nauka, Moscow (in Russian). English translation: Springer-Verlag, Berlin etc., 1989.Google Scholar
  10. 10.
    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.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • A. D. Bruno
    • 1
  1. 1.Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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