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Differential Equations, Vol. 40, No. 5, 2004, pp. 672–685. Translated from Differentsial’nye Uravneniya, Vol. 40, No. 5, 2004, pp. 626–638. Original Russian Text Copyright c 2004 by Petrov. ORDINARY DIFFERENTIAL EQUATIONS Asymptotic Methods for Solving the Hamilton Equations with the Use of a Parametrization of Canonical Transformations A. G. Petrov Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia Received April 10, 2003 We suggest a new method for constructing asymptotic solutions of Hamiltonian systems of ordinary differential equations under the assumption that the Hamiltonian is a periodic function of time and can be represented by a series in powers of a small parameter. We present algorithms for the solution of both the direct problem of constructing the asymptotic series for the phase flow map on the basis of a given Hamiltonian and the inverse problem of constructing the Hamiltonian on the basis of a given phase flow map. Our algorithms are based on a new representation of canonical changes of variables in parametric form. A general time-dependent change of variables is expressed via a function of parameters. For a time-independent canonical change of variables, the total differential of this function coincides with the differential of
Differential Equations – Springer Journals
Published: Oct 17, 2004
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