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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 5(413), Pages 147–176 (Mi umn9524)  

This article is cited in 5 scientific papers (total in 5 papers)

On analytic insolubility of the stability problem on the plane

N. B. Medvedevaab

a Chelyabinsk State University
b South-Ural State University

Abstract: This is a survey on questions involving algebraic and analytic solubility of the problem of stability of a singular point of a vector field on the plane, and in particular of the problem of distinguishing between a centre and a focus. It is proved that the stability problem on the plane is analytically insoluble.
Bibliography: 30 titles.

Keywords: vector field, monodromic singular point, focus, centre, monodromy transformation, Newton diagram, blow-up of singularities.

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/rm9524

Full text: PDF file (743 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2013, 68:5, 923–949

Bibliographic databases:

UDC: 517.9
MSC: Primary 37C10; Secondary 37C75, 58K45
Received: 17.02.2013

Citation: N. B. Medvedeva, “On analytic insolubility of the stability problem on the plane”, Uspekhi Mat. Nauk, 68:5(413) (2013), 147–176; Russian Math. Surveys, 68:5 (2013), 923–949

Citation in format AMSBIB
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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. A. A. Ershov, M. I. Rusanova, “Asymptotics of multidimensional integrals with singular dependence on a small parameter”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 72–80  mathnet  crossref  mathscinet  isi  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
    5. N. B. Medvedeva, V. A. Viktorova, “Priblizhennoe vychislenie integralov Adamara spetsialnogo vida”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 398–411  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
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