On the global center of planar polynomial differential systems and the related problems

DOI10.11948/20220157MaRDI QIDQ6597358

Hongjin He, Dongmei Xiao

Publication date: 3 September 2024

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

zbMATH Keywords

differential systemsintegrableglobal centersufficient and necessary conditionsplanar polynomials

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Cites Work

• Unnamed Item
• Integrability of dynamical systems: algebra and analysis
• Monodromic unbounded polycycles
• Limit cycles bifurcating from the period annulus of quasi-homogeneous centers
• Center problem for several differential equations via Cherkas' method
• On polynomial Hamiltonian planar vector fields
• Recent advances on determining the number of real roots of parametric polynomials
• Perturbation theory of a symmetric center within Liénard equations
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Centers: their integrability and relations with the divergence
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

Related Items (5)

Global centers of a class of cubic polynomial differential systems ⋮ Nilpotent global centers of generalized polynomial Kukles system with degree three ⋮ Global phase portraits of generalized polynomial Liénard system with a unique equilibrium and a periodic annulus ⋮ The number of limit cycles near a double homoclinic loop for a near-Hamiltonian system ⋮ New families of global cubic centers

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