The problem of center for resonant singular points of polynomial vector fields
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Publication:1361821
DOI10.1006/jdeq.1997.3260zbMath0885.34034OpenAlexW2155899859MaRDI QIDQ1361821
Publication date: 9 September 1997
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jdeq.1997.3260
Related Items (45)
Integrability of resonant saddles in a complex differential system ⋮ The solution of the \(1:-3\) resonant center problem in the quadratic case ⋮ Analytic integrability of certain resonant saddle ⋮ An algebraic model for the center problem ⋮ On integrability and linearizability of persistent \(p:- q\) resonant systems ⋮ \(1: - 3\) resonant centers on \(\mathbb{C}^2\) with homogeneous cubic nonlinearities ⋮ On the integrability of Liénard systems with a strong saddle ⋮ On the formal integrability problem for planar differential systems ⋮ On a conjecture on the integrability of Liénard systems ⋮ Local integrability and linearizability of a \((1:-1:-1)\) resonant quadratic system ⋮ Generalized isochronous centers for complex systems ⋮ The \({1:-q}\) resonant center problem for certain cubic Lotka-Volterra systems ⋮ The center problem for a \({1:-4}\) resonant quadratic system ⋮ The Poincaré center problem ⋮ Integrability and linearizability of symmetric three-dimensional quadratic systems ⋮ The Sibirsky component of the center variety of polynomial differential systems. ⋮ Essential variables in the integrability problem of planar vector fields ⋮ Linearizability of homogeneous quartic polynomial systems with \(1:-2\) resonance ⋮ The generalized center problem of resonant infinity for a polynomial differential system ⋮ Integrability and linearizability of the Lotka-Volterra systems. ⋮ On the saddle order of polynomial differential systems at a resonant singular point ⋮ Integrability of Lotka-Volterra type systems of degree 4 ⋮ Cyclicity of some analytic maps ⋮ The center and cyclicity problems for some analytic maps ⋮ Integrability and linearizability of three dimensional vector fields ⋮ Analytic integrability around a nilpotent singularity ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ Integrability conditions of a resonant saddle in Liénard-like complex systems ⋮ Linearizability of the polynomial differential systems with a resonant singular point ⋮ Analytical integrability problem for perturbations of cubic Kolmogorov systems ⋮ The integrability conditions for two cubic vector fields ⋮ An explicit expression for the first return map in the center problem ⋮ Bautin ideal of a cubic map ⋮ Cauchy-type integrals of algebraic functions ⋮ Integrability conditions for Lotka-Volterra planar complex quintic systems ⋮ Center conditions at infinity for Abel differential equations ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ The integrability of a class of cubic Lotka-Volterra systems ⋮ The generalized center problem of degenerate resonant singular point ⋮ Integrability and linearizability for Lotka-Volterra systems with the \(3 : -q\) resonant saddle point ⋮ Generalized singular point quantity and integrability of degenerate resonant singular 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 ⋮ Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system
Cites Work
- Quadratic systems with center and their perturbations
- The classification of reversible cubic systems with center
- Algebraic nonsolvability andalmost algebraic solvability of the center- focus problem
- Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$
- On the number of invariant lines for polynomial vector fields
- Eleven small limit cycles in a cubic vector field
- Reduction of Singularities of the Differential Equation Ady = Bdx
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