Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems

DOI10.1016/j.na.2010.04.059zbMath1201.34050OpenAlexW1964849984MaRDI QIDQ984100

Cristóbal García, Manuel Reyes, Antonio Algaba

Publication date: 13 July 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.04.059

zbMATH Keywords

quasi-homogeneous vector fieldKowalevskaya exponentsrational integrability

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 (10)

Invariant curves and analytic integrability of a planar vector field ⋮ On the formal integrability problem for planar differential 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 ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Global dynamics of planar quasi-homogeneous differential systems ⋮ Generalized analytic integrability of a class of polynomial differential systems in \(\mathbb{C}^2\) ⋮ A survey on the Kovalevskaya exponents and their applications ⋮ Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems

Cites Work

• Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3
• On non-integrability of general systems of differential equations
• The center problem for a family of systems of differential equations having a nilpotent singular point
• On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations
• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals

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