This article is cited in 8 papers

On analytic insolubility of the stability problem on the plane

N. B. Medvedeva<sup>ab

a</sup> 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.

UDC: 517.9

MSC: Primary 37C10; Secondary 37C75, 58K45

Received: 17.02.2013

DOI: 10.4213/rm9524

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

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