
Mathematics
Calculation of the power series coefficients of a monodromy map in the Maple environment
N. B. Medvedeva^{}, M. A. Sosnovskaya^{} ^{} Chelyabinsk State University, Chelyabinsk, Russia
Abstract:
The article proposes a computer algorithm in Maple for the coefficients calculation of the asymptotic series for the monodromic singular point monodromy transformation of a vector
field in the plane, when its Newton diagram consists of one nondegenerate edge. The coefficients of the asymptotic series are expressed in terms of improper integrals
for functions, which are based on a Taylor decomposition of the vector field at the singular point. In view of the complexity of the integrands in these integrals
their computing in the environment of Maple is impossible. In this paper a method of the calculation of these coefficients using the solving of some differential equations is proposed.
The program in the environment of Maple, which calculates these coefficients, is offered. An example of the computing is given.
Keywords:
monodromic singular point, focus, center, monodromy transformation, Newton diagram, Maple.
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UDC:
517.9 Received: 18.05.2017 Revised: 24.06.2017
Citation:
N. B. Medvedeva, M. A. Sosnovskaya, “Calculation of the power series coefficients of a monodromy map in the Maple environment”, Chelyab. Fiz.Mat. Zh., 2:2 (2017), 181–192
Citation in format AMSBIB
\Bibitem{MedSos17}
\by N.~B.~Medvedeva, M.~A.~Sosnovskaya
\paper Calculation of the power series coefficients of a monodromy map in the Maple environment
\jour Chelyab. Fiz.Mat. Zh.
\yr 2017
\vol 2
\issue 2
\pages 181192
\mathnet{http://mi.mathnet.ru/chfmj54}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3673249}
\elib{http://elibrary.ru/item.asp?id=29777083}
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