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The Methods of Computer Algebra and the Arnold-Moser Theorem

In: Computer Algebra in Scientific Computing CASC 2001

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  • E. A. Grebenikov

    (University of Podlasie, CS RAS)

Abstract

It is well known that the problem of stability of the particular solutions of Hamilton systems in Lyapunov sense cannot be solved within the framework of the classical stability theory. For Hamilton systems with two degrees of freedom the above problem is investigated within the framework of the KAM theory on the basis of the well-known theorem of Arnold-Moser about stability in the so-called “elliptic case”. We formulate and investigate the problem of the stability of equilibrium state for dynamic models termed restricted problems of many (n > 3) bodies. All necessary analytical transformations, switching of linearization of the differential equations, and the normalization of hamiltonians after Birkhoff are executed with the help of the System of Symbolical Calculations (SSC) “Mathematica”.

Suggested Citation

  • E. A. Grebenikov, 2001. "The Methods of Computer Algebra and the Arnold-Moser Theorem," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC 2001, pages 297-308, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56666-0_22
    DOI: 10.1007/978-3-642-56666-0_22
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