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Symbolic Computation of a Homological Equation of an Arbitrary Order and Reduction of Hamiltonian System to Its Normal Form

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Abstract

A procedure for deriving homological equations of an arbitrary order is considered. Solutions of these equations are used in the iterative procedure of invariant normalization of the Hamiltonian in the neighborhood of equilibrium state. Specific features of the implementation of the algorithm for reducing to normal form using modern computer algebra systems are discussed. The normalization procedure is applied to the Hamiltonian of the Hill problem written in terms of scaled regular variables. The Hill problem normal form thus obtained can be used for finding analyticity sets of the normalizing transformation.

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ACKNOWLEDGMENTS

The author is grateful to Professor A. D. Bruno for support and useful discussion of this paper.

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Correspondence to A. B. Batkhin.

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Translated by A. Klimontovich

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Batkhin, A.B. Symbolic Computation of a Homological Equation of an Arbitrary Order and Reduction of Hamiltonian System to Its Normal Form. Program Comput Soft 48, 65–72 (2022). https://doi.org/10.1134/S0361768822020037

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  • DOI: https://doi.org/10.1134/S0361768822020037

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