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.
\Bibitem{Med13}
\by N.~B.~Medvedeva
\paper On analytic insolubility of the stability problem on the plane
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 5
\pages 923--949
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Linking options:
https://www.mathnet.ru/eng/rm9524
https://doi.org/10.1070/RM2013v068n05ABEH004861
https://www.mathnet.ru/eng/rm/v68/i5/p147
This publication is cited in the following 8 articles:
D. N. Cherginets, “System without Characteristic Directions with a Nonanalytic Center Condition”, Diff Equat, 59:12 (2023), 1598
N. B. Medvedeva, “Approximate calculation of the coefficients of the Dulac series”, Russian Math. (Iz. VUZ), 65:10 (2021), 31–43
N. B. Medvedeva, “The problem of distinguishing between a centre and a focus in the space of vector fields with given Newton diagram”, Sb. Math., 211:10 (2020), 1399–1446
N. B. Medvedeva, V. A. Viktorova, “Granitsa ustoichivosti v odnom prostom klasse monodromnykh rostkov”, Chelyab. fiz.-matem. zhurn., 4:3 (2019), 276–284
N. B. Medvedeva, V. A. Viktorova, “Priblizhennoe vychislenie
integralov Adamara spetsialnogo vida”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 398–411
N. B. Medvedeva, M. A. Sosnovskaya, “Vychislenie koeffitsientov stepennogo ryada preobrazovaniya monodromii v sisteme Maple”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 181–192
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
N. B. Medvedeva, “Asimptoticheskoe razlozhenie preobrazovaniya monodromii”, Chelyab. fiz.-matem. zhurn., 1:1 (2016), 59–72
Citation in format AMSBIB
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