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Algebraic aspects of perturbation theories

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Abstract

In this paper the following problems are considered: Hori's perturbation equations, the composition of two Lie series, the elimination of geometrical (virtual) singularities in perturbation theory, the connection between the methods of Hori and Deprit. The analysis is based on an isomorphism between the Lie algebra of the non-associative algebra of vector fields and a Lie algebra of linear operators. All linear operators, however, form an associative algebra.

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Authors and Affiliations

  1. Seminar für Angewandte Mathematik ETH, Zürich, Switzerland

    F. Spirig

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  1. F. Spirig
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Spirig, F. Algebraic aspects of perturbation theories. Celestial Mechanics 20, 343–354 (1979). https://doi.org/10.1007/BF01230403

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  • DOI: https://doi.org/10.1007/BF01230403

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