The center problem for a linear center perturbed by homogeneous polynomials
From MaRDI portal
Publication:882716
DOI10.1007/s10114-005-0623-4zbMath1124.34326OpenAlexW2129935427MaRDI QIDQ882716
Publication date: 24 May 2007
Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10114-005-0623-4
Periodic solutions to ordinary differential equations (34C25) 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 (25)
The solution of the \(1:-3\) resonant center problem in the quadratic case ⋮ Centers for a class of generalized quintic polynomial differential systems ⋮ Lower bounds for the local cyclicity for families of centers ⋮ On persistent centers ⋮ Unnamed Item ⋮ Small-amplitude limit cycles of certain planar differential systems ⋮ An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems ⋮ An algorithmic approach to small limit cycles of nonlinear differential systems: the averaging method revisited ⋮ Centers for trigonometric Abel equations ⋮ Nondegenerate and nilpotent centers for a cubic system of differential equations ⋮ Minimum number of ideal generators for a linear center perturbed by homogeneous polynomials ⋮ Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers ⋮ Limit cycle bifurcations from a non-degenerate center ⋮ Center problem for systems with two monomial nonlinearities ⋮ Centers of weight-homogeneous polynomial vector fields on the plane ⋮ Integrability conditions of a weak saddle in generalized Liénard-like complex polynomial differential systems ⋮ Higher order limit cycle bifurcations from non-degenerate centers ⋮ Lower bounds for the local cyclicity of centers using high order developments and parallelization ⋮ Global C∞ integrability of quartic–linear polynomial differential systems ⋮ Centers and isochronous centers for generalized quintic systems ⋮ Reversible nilpotent centers with cubic homogeneous nonlinearities ⋮ Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers ⋮ Center conditions and integrable forms for the Poincaré problem ⋮ On the center-focus problem for a family of high-order polynomial differential systems ⋮ A general class of centers for the Poincaré problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
- Singularities of vector fields on the plane
- On the integrability of two-dimensional flows
- Algebraic properties of the Lyapunov and period constants
- Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
- Cubic vector fields symmetric with respect to a center
- Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
- Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
- The number of limit cycles of certain polynomial differential equations
- Integrable systems in the plane with center type linear part
- Eleven small limit cycles in a cubic vector field
- A class of integrable polynomial vector fields
This page was built for publication: The center problem for a linear center perturbed by homogeneous polynomials
