The solution of the \(1:-3\) resonant center problem in the quadratic case

DOI10.1016/j.amc.2014.03.147zbMath1334.34067OpenAlexW2010938799MaRDI QIDQ275034

Brigita Ferčec, Maša Dukarić, Jaume Giné

Publication date: 25 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.03.147

zbMATH Keywords

modular arithmeticsfirst integralquadratic systemsresonant center problem

Mathematics Subject Classification ID

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

Related Items (3)

On integrability and linearizability of persistent \(p:- q\) resonant systems ⋮ The center problem for a \({1:-4}\) resonant quadratic system ⋮ The complexity of generalized center problem

Uses Software

• SINGULAR
• primdec

Cites Work

• On the formal integrability problem for planar differential systems
• The \({1:-q}\) resonant center problem for certain cubic Lotka-Volterra systems
• Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities
• An approach to solving systems of polynomials via modular arithmetics with applications
• The center problem for a linear center perturbed by homogeneous polynomials
• The center problem for a \(2:-3\) resonant cubic Lotka-Volterra system
• Integrability conditions for Lotka-Volterra planar complex quintic systems
• The problem of center for resonant singular points of polynomial vector fields
• Modular algorithms for computing Gröbner bases.
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• Integrability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities
• Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system
• \(1: - 3\) resonant centers on \(\mathbb{C}^2\) with homogeneous cubic nonlinearities
• On the center problem for \(p:-q\) resonant polynomial vector fields
• The Resonant Center Problem for a 2:-3 Resonant Cubic Lotka–Volterra System
• The Center and Cyclicity Problems
• Linearizability conditions for Lotka–Volterra planar complex cubic systems
• Unnamed Item

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