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Voisinage et stabilité des solutions périodiques des systèmes hamiltoniens

Abstract : In the dynamical systems the study of the vicinity and the stability of a periodic solution begins usually by the “first-order study” of the variational system. The first step leads either to the exponential stability or to the exponential instability or to the “critical case” in which the largest Liapounov characteristic exponent is zero. In this third case it becomes necessary to consider the higher order terms. Most critical cases appear in Hamiltonian, problems and the study of large order terms begins by several simplifications that are presented in chapters I and II. These simplifications lead to the near –resonance theorem and to the adjacent useful notions : quasi-integrals, positive resonances etc … that allow a general classification of the types of stability and instability. The chapters III and IV apply these theoretical results to the Lagrangian motions of the 3-body problem. The results are very different according the case of interest. The restricted circular problem is entirely solved (planar case) or almost entirely solved (three-dimensional case).
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Larbi El Bakkali. Voisinage et stabilité des solutions périodiques des systèmes hamiltoniens. Astrophysique [astro-ph]. Observatoire de Paris, 1990. Français. ⟨tel-02095283⟩

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