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Approximate Calculation of the Coefficients of the Dulac Series

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Abstract

An algorithm for the approximate calculation of the coefficients of the Dulac series (an asymptotic series of the monodromy transformation) in the space of vector fields with a Newton diagram containing more than one edge and a monodromic singular point is proposed. The conditions for the applicability of this algorithm are obtained. The algorithm is implemented in the MAPLE package. Examples are given for the case of a Newton diagram consisting of two edges.

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Funding

The work was supported by the Russian Foundation for Basic Research, grant no. 17-01-00739a.

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Author notes

  1. N. B. Medvedeva died before publication of this work was completed.

Authors and Affiliations

  1. Chelyabinsk State University, 129 Br. Kashirinykh str., 454001, Chelyabinsk, Russia

    N. B. Medvedeva

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  1. N. B. Medvedeva
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 10, pp. 37–50.

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Medvedeva, N.B. Approximate Calculation of the Coefficients of the Dulac Series. Russ Math. 65, 31–43 (2021). https://doi.org/10.3103/S1066369X21100030

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  • DOI: https://doi.org/10.3103/S1066369X21100030

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