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Frontmatter -1 Chapter I Physical aspects of dynamical systems -1 Chapter II Variational principles and applications -1 Chapter III Formal aspects of dynamics -1 Chapter IV Stability of periodic motions -1 Chapter V Existence of periodic motions -1 Chapter VI Application of Poincare's geometric theorem 1 1. Periodic motions near generalized equilibrium (m = 1). 1 2. Proof of the lemma of section 1. 5 3. Periodic motions near a periodic motion (m = 2). 10 4. Some remarks. 13 5. The geometric theorem of Poincaré. 16 6. The billiard ball problem. 20 7. The corresponding transformation T. 22 8. Area-preserving property of T. 24 9. Applications to billiard ball problem. 27 10. The geodesic problem. Construction of a transformation TT*. 31 11. Application of Poincaré's theorem to problem. 36 Chapter VII General theory of dynamical systems -1 Chapter VIII The case of two degrees of freedom -1 Chapter IX The problem of three bodies -1 Endmatter -1

Author

北弘传媒

Language

ZH