Complete study on a bi-center problem for the \(Z_2\)-equivariant cubic vector fields

DOI10.1007/s10114-011-8412-8zbMath1364.34040OpenAlexW2095496924MaRDI QIDQ475748

Yi-rong Liu, Ji-Bin Li

Publication date: 27 November 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-011-8412-8

zbMATH Keywords

center probleminvariant integralfocal valuecubic polynomial systemintegral factorLiapunov constant

Mathematics Subject Classification ID

Related Items (14)

Simultaneity of centres in ℤ _q -equivariant systems ⋮ Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems ⋮ Isochronicity of a \(\mathbb{Z}_2\)-equivariant quintic system ⋮ Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Symmetric centers on planar cubic differential systems ⋮ Complete classification on center of cubic planar systems symmetric with respect to a straight line ⋮ \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ \(Z_2\)-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields ⋮ Bi-center problem and Hopf cyclicity of a cubic Liénard system ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points ⋮ Simultaneity of centres in double-reversible planar differential systems ⋮ Isochronicity of bi-centers for symmetric quartic differential systems

Cites Work

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• Integrability of plane quadratic vector fields
• Theory of values of singular point in complex autonomous differential systems
• Cubic systems and Abel equations
• Center problem for several differential equations via Cherkas' method
• An explicit expression of the first Lyapunov and period constants with applications
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
• A cubic system with twelve small amplitude limit cycles
• The centre and isochronicity problems for some cubic systems
• A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS

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