Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points

DOI10.1016/j.jde.2020.06.036zbMath1450.37052OpenAlexW3037645376MaRDI QIDQ778244

Feng Li, Yun Tian, Pei Yu, Yin Lai Jin

Publication date: 2 July 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.06.036

zbMATH Keywords

integrabilityinvariant algebraic curvelinearizabilitycomplex centercomplex isochronous center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38)

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Cites Work

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• Bifurcation of limit cycles in a quintic system with ten parameters
• Complete study on a bi-center problem for the \(Z_2\)-equivariant cubic vector fields
• \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles
• New results on the study of \(Z_q\)-equivariant planar polynomial vector fields
• A cubic system with thirteen limit cycles
• Global bifurcations in a disturbed Hamiltonian vector field approaching a 3:1 resonant Poincaré map. I
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• Global bifurcations in a perturbed cubic system with \(Z_ 2\)-symmetry
• The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields
• Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields
• 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
• Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems
• A cubic system with twelve small amplitude limit cycles
• Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems
• Isochronicity for a \(Z_{2}\)-equivariant cubic system
• EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM
• Simultaneity of centres in ℤ _q -equivariant systems
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM