Local behavior of planar analytic vector fields via integrability

DOI10.1016/j.jmaa.2011.06.062zbMath1237.34035OpenAlexW2087957477MaRDI QIDQ641580

Antoni Ferragut, Maria Jesus Alvarez

Publication date: 24 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.06.062

zbMATH Keywords

blow-upplanar analytic vector fieldgeneralized rational first integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (3)

Some new results on Darboux integrable differential systems ⋮ A SURVEY ON THE BLOW UP TECHNIQUE ⋮ Bounding the number of remarkable values via Jouanolou's theorem

Cites Work

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• A new algorithm for finding rational first integrals of polynomial vector fields
• Multiplicity of invariant algebraic curves in polynomial vector fields
• Singularities of vector fields on the plane
• Darboux integrability and the inverse integrating factor.
• On the Poincaré problem
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• On the remarkable values of the rational first integrals of polynomial vector fields
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• A SURVEY ON THE BLOW UP TECHNIQUE
• Reduction of Singularities of the Differential Equation Ady = Bdx
• Planar analytic vector fields with generalized rational first integrals

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