On the remarkable values of the rational first integrals of polynomial vector fields

DOI10.1016/j.jde.2007.05.002zbMath1132.34030OpenAlexW1966306237WikidataQ126262120 ScholiaQ126262120MaRDI QIDQ2455611

Jaume Llibre, Antoni Ferragut

Publication date: 25 October 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.05.002

zbMATH Keywords

inverse integrating factorpolynomial vector fieldrational first integralremarkable valueremarkable curveremarkable factor

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

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Cites Work

• Unnamed Item
• Unnamed Item
• Polynomial differential systems having a given Darbouxian first integral
• Multiplicity of invariant algebraic curves in polynomial vector fields
• On the integrability of two-dimensional flows
• Darboux integrability and the inverse integrating factor.
• Configurations of limit cycles and planar polynomial vector fields.
• Polynomial inverse integrating factors for polynomial vector fields
• Integral invariants and limit sets of planar vector fields
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• On the nonexistence, existence and uniqueness of limit cycles
• Vector fields, invariant varieties and linear systems.
• On the vanishing set of inverse integrating factors

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