Geodesic
Approximate calculation of the coefficients of the Dulac series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 37-50

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An algorithm for the approximate calculation of the coefficients of the Dulac series (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.
Mots-clés : Monodromic singular point, monodromy transformation
Keywords: focus, center, Dulac series, correspondence mapping, Newton diagram, asymptotic representation, Hadamard integral. 
@article{IVM_2021_10_a2,
     author = {N. B. Medvedeva},
     title = {Approximate calculation of the coefficients of the {Dulac} series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--50},
     publisher = {mathdoc},
     number = {10},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_10_a2/}
}
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N. B. Medvedeva. Approximate calculation of the coefficients of the Dulac series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2021), pp. 37-50. http://geodesic.mathdoc.fr/item/IVM_2021_10_a2/