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Russian Mathematical Surveys, 2013, Volume 68, Issue 5, Pages 923–949
DOI: https://doi.org/10.1070/RM2013v068n05ABEH004861 (Mi rm9524) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On analytic insolubility of the stability problem on the plane

N. B. Medvedevaab

a Chelyabinsk State University
b South-Ural State University
English version PDF (680 kB) Citations (8)
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DOI: https://doi.org/10.1070/RM2013v068n05ABEH004861
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
Received: 17.02.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2013, Volume 68, Issue 5(413), Pages 147–176
DOI: https://doi.org/10.4213/rm9524
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 37C10; Secondary 37C75, 58K45
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Russian version PDF:206
    English version PDF:13
    References:48
    First page:23
     
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