Titlebook: Mathematical Aspects of Classical and Celestial Mechanics; V. I. Arnold,V. V. Kozlov,A. I. Neishtadt Book 19972nd edition Springer-Verlag

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Nonintegrable Systems,s, but they simply do not exist, since the trajectories of Hamiltonian systems, generally speaking, do not lie on low-dimensional invariant manifolds. We have in mind, of course, integrals which exist on the entire phase space: a complete set of independent first integrals always exists in a small neighborhood of a nonsingular point.

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Theory of Small Oscillations,g the theory of normal forms of Poincare-Birkhoff. This theory is an analog of perturbation theory (Ch. 5, §2). Here the linearized system plays the role of the unperturbed system with respect to the original one. In this chapter we describe the basic elements of such an approach.

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V. I. Arnold,V. V. Kozlov,A. I. Neishtadt could be used for the highest levels of control systems. We have examined the performance of different neural networks in traditional image recognition tasks and in problems that appear in micromechanical m978-3-642-42611-7978-3-642-02535-8

Cursory

V. I. Arnold,V. V. Kozlov,A. I. Neishtadt could be used for the highest levels of control systems. We have examined the performance of different neural networks in traditional image recognition tasks and in problems that appear in micromechanical m978-3-642-42611-7978-3-642-02535-8

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Symmetry Groups and Reduction (Lowering the Order),

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Mathematical Aspects of Classical and Celestial Mechanics