Geodesic
Calculation of the power series coefficients of a monodromy map in the Maple environment
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 181-192

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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 non-degenerate 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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     author = {N. B. Medvedeva and M. A. Sosnovskaya},
     title = {Calculation of the power series coefficients of a monodromy map in the {Maple} environment},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {181--192},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a3/}
}
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N. B. Medvedeva; M. A. Sosnovskaya. Calculation of the power series coefficients of a monodromy map in the Maple environment. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 181-192. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a3/