Local phase portraits through the Newton diagram of a vector field

DOI10.1007/s10114-015-3663-4zbMath1330.34047OpenAlexW638658689MaRDI QIDQ887464

Isabel Checa, Antonio Algaba, Manuel Reyes, Cristóbal García

Publication date: 26 October 2015

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-015-3663-4

zbMATH Keywords

monodromyphase portraitsquasi-homogeneous vector fieldseparatrices

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) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Cites Work

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• A new algorithm for determining the monodromy of a planar differential system
• Characterization of a monodromic singular point of a planar vector field
• Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra
• Separatrices at singular points of planar vector fields
• Singularities of vector fields on the plane
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• The integrability problem for a class of planar systems

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