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 Chelyab. Fiz.-Mat. Zh., 2016, Volume 1, Issue 1, Pages 59–72 (Mi chfmj7)

Mathematics

Asymptotic expansion of a monodromy map

N. B. Medvedevaab

a Chelyabinsk State University, Chelyabinsk, Russia
b South Ural State University (National Research University), Chelyabinsk, Russia

Abstract: In the paper we compute the asymptotic series of the monodromy transformation of a monodromic singular point of a vector field in the plane when its Newton diagram consists of a single non-degenerate edge. The method of a resolution of singularities via Newton diagram is applied. A hypothesis about the existence of an algorithm for calculating the coefficients of correspondence maps and monodromy transformation containing no operation limit is put forward. This conjecture has been proved in the case of a single non-degenerate edge of the Newton diagram, as well as for the first two coefficients in the asymptotic expansion of the correspondence map in the first quadrant of the plane (as well as the monodromy transformation) in the case where the Newton diagram of the vector field consists of two non-degenerate edges.

Keywords: monodromic singular point, resolution of singularities, focus, center, monodromy transformation, Newton diagram.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00512-à

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UDC: 517.9
Revised: 01.02.2016

Citation: N. B. Medvedeva, “Asymptotic expansion of a monodromy map”, Chelyab. Fiz.-Mat. Zh., 1:1 (2016), 59–72

Citation in format AMSBIB
\Bibitem{Med16} \by N.~B.~Medvedeva \paper Asymptotic expansion of a monodromy map \jour Chelyab. Fiz.-Mat. Zh. \yr 2016 \vol 1 \issue 1 \pages 59--72 \mathnet{http://mi.mathnet.ru/chfmj7} \elib{http://elibrary.ru/item.asp?id=27541607} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. B. Medvedeva, M. A. Sosnovskaya, “Vychislenie koeffitsientov stepennogo ryada preobrazovaniya monodromii v sisteme Maple”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 181–192
2. N. B. Medvedeva, V. A. Viktorova, “Granitsa ustoichivosti v odnom prostom klasse monodromnykh rostkov”, Chelyab. fiz.-matem. zhurn., 4:3 (2019), 276–284
3. N. B. Medvedeva, V. A. Viktorova, “Priblizhennoe vychislenie integralov Adamara spetsialnogo vida”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 398–411
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