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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 2, Pages 35–52 (Mi izv7984)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotics of the monodromy transformation in certain classes of monodromy germs

A. S. Voronin, N. B. Medvedeva

Chelyabinsk State University

Abstract: We calculate the second term of the asymptotics of the monodromy transformation of a monodromic singular point of an analytic vector field on a plane whose Newton diagram consists of one or two edges. In the cases under consideration the principal term of the monodromy transformation coincides with the identity function. The case of two edges is characterized by the fact that, as a result of blowing up the singularity by the Newton diagram, a singular point emerges that is a degenerate saddle. The results obtained make it possible to state a sufficient condition for the existence of a focus and to construct the stability boundary in the classes of vector fields under consideration.

Keywords: monodromic singular point, blowing up singularities, focus, centre, monodromy transformation.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00587-а
Ministry of Education and Science of the Russian Federation 02.740.110612


DOI: https://doi.org/10.4213/im7984

Full text: PDF file (563 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:2, 253–270

Bibliographic databases:

UDC: 517.9
MSC: 37C10, 34C05, 34D20, 58K45
Received: 29.03.2012
Revised: 04.07.2012

Citation: A. S. Voronin, N. B. Medvedeva, “Asymptotics of the monodromy transformation in certain classes of monodromy germs”, Izv. RAN. Ser. Mat., 77:2 (2013), 35–52; Izv. Math., 77:2 (2013), 253–270

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. B. Medvedeva, “On analytic insolubility of the stability problem on the plane”, Russian Math. Surveys, 68:5 (2013), 923–949  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. N. B. Medvedeva, “Asimptoticheskoe razlozhenie preobrazovaniya monodromii”, Chelyab. fiz.-matem. zhurn., 1:1 (2016), 59–72  mathnet  elib
    3. N. B. Medvedeva, M. A. Sosnovskaya, “Vychislenie koeffitsientov stepennogo ryada preobrazovaniya monodromii v sisteme Maple”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 181–192  mathnet  mathscinet  elib
    4. N. B. Medvedeva, V. A. Viktorova, “Granitsa ustoichivosti v odnom prostom klasse monodromnykh rostkov”, Chelyab. fiz.-matem. zhurn., 4:3 (2019), 276–284  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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