The problem of distinguishing between a centre and a focus in the space of vector fields with given Newton diagram

DOI10.1070/SM9186zbMath1462.34052OpenAlexW3043578867MaRDI QIDQ5149924

N. B. Medvedeva

Publication date: 9 February 2021

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm9186

zbMATH Keywords

Newton diagrammonodromic singular pointtransition mapmonodromy transformationDulac series

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (1)

Approximate calculation of the coefficients of the Dulac series

Cites Work

• The asymptotics to the return map of a singular point with fixed Newton diagram
• Principal term of the monodromy transformation of a monodromic singular point is linear
• Singularities of vector fields on the plane
• Algebraically and analytically solvable local problems in the theory of ordinary differential equations
• The principal term of the asymptotics of the monodromy transformation: Computation in accordance with blow-up geometry
• Local problems of analysis
• On the analytic solvability of the problem of distinguishing between center and focus
• Algebraic nonsolvability andalmost algebraic solvability of the center- focus problem
• Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations
• Poincaré map for some polynomial systems of differential equations
• Symétrie et forme normale des centres et foyers dégénérés
• Asymptotics of the monodromy transformation in certain classes of monodromy germs
• On analytic insolubility of the stability problem on the plane
• Finiteness theorems for limit cycles
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