\(1: - 3\) resonant centers on \(\mathbb{C}^2\) with homogeneous cubic nonlinearities

DOI10.1016/j.camwa.2008.04.009zbMath1165.34334OpenAlexW2079543524MaRDI QIDQ2389733

Valery G. Romanovski, Zhaoping Hu, Douglas S. Shafer

Publication date: 18 July 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.04.009

zbMATH Keywords

center varietyfirst integralresonant centerpolynomial systems of differential equationsDarboux integration

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (14)

The solution of the \(1:-3\) resonant center problem in the quadratic case ⋮ Integrability of fractional order generalized systems with \(p:-q\) resonance ⋮ On the formal integrability problem for planar differential systems ⋮ The \({1:-q}\) resonant center problem for certain cubic Lotka-Volterra systems ⋮ The center problem for a \(2:-3\) resonant cubic Lotka-Volterra system ⋮ Essential variables in the integrability problem of planar vector fields ⋮ An approach to solving systems of polynomials via modular arithmetics with applications ⋮ On the saddle order of polynomial differential systems at a resonant singular point ⋮ A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS ⋮ The integrability of a class of cubic Lotka-Volterra systems ⋮ Integrability and linearizability for Lotka-Volterra systems with the \(3 : -q\) resonant saddle point ⋮ The complexity of generalized center problem ⋮ Integrability and generalized center problem of resonant singular point ⋮ Local integrability and linearizability of three-dimensional Lotka-Volterra systems

Uses Software

• SINGULAR
• primdec

Cites Work

• Unnamed Item
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• Elimination methods
• The problem of center for resonant singular points of polynomial vector fields
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems
• On the center problem for \(p:-q\) resonant polynomial vector fields
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• The centre and isochronicity problems for some cubic systems
• Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in \(\mathbb C^2\)

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