Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)

DOI10.1360/03ys9029zbMath1217.37049OpenAlexW1571780622MaRDI QIDQ551775

Xiang Zhang

Publication date: 21 July 2011

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1360/03ys9029

zbMATH Keywords

invariant algebraic curveholomorphic foliationrational first integralcubic limit cycle

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (7)

Liouvillian integrability versus Darboux polynomials ⋮ Algebraic limit cycles for quadratic polynomial differential systems ⋮ On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity ⋮ The 16th Hilbert problem on algebraic limit cycles ⋮ Darboux integrability and algebraic limit cycles for a class of polynomial differential systems ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ Algebraic Limit Cycles on Quadratic Polynomial Differential Systems

Cites Work

• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• The Poincaré problem in the nondicritical case
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Proximity inequalities and bounds for the degree of invariant curves by foliations of ℙ_{ℂ}²
• On a Result of Darboux
• Invariant algebraic surfaces of the Lorenz system
• Invariant algebraic curves and rational first integrals for planar polynomial vector fields
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