Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3

DOI10.1016/j.jmaa.2006.09.066zbMath1124.34015OpenAlexW1968263269MaRDI QIDQ878498

Jaume Llibre, Laurent Cairó

Publication date: 26 April 2007

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

Full work available at URL: http://ddd.uab.cat/record/221041

zbMATH Keywords

polynomial first integralKowalevskaya exponentsweight-homogeneous polynomial system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (15)

Classification and counting of planar quasi-homogeneous differential systems through their weight vectors ⋮ On the centers of the weight-homogeneous polynomial vector fields on the plane ⋮ Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems ⋮ On the polynomial differential systems having polynomial first integrals ⋮ Integrability of two dimensional quasi-homogeneous polynomial differential systems ⋮ Centers of quasi-homogeneous polynomial planar systems ⋮ Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ Center of planar quintic quasi-homogeneous polynomial differential systems ⋮ Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree ⋮ Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Global dynamics of planar quasi-homogeneous differential systems ⋮ Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems ⋮ Limit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems

Cites Work

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• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• On the polynomial first integrals of the (a,b,c) Lotka–Volterra system
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals

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