Geodesic
On analytic insolubility of the stability problem on the plane
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 5, pp. 923-949

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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, focus, Newton diagram, blow-up of singularities.
Mots-clés : monodromic singular point, centre, monodromy transformation 
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N. B. Medvedeva. On analytic insolubility of the stability problem on the plane. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 5, pp. 923-949. http://geodesic.mathdoc.fr/item/RM_2013_68_5_a3/