Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System

DOI10.1142/S0218127421501170zbMath1481.34042arXiv2009.08042OpenAlexW3175770059MaRDI QIDQ4997488

Yusen Wu

Publication date: 29 June 2021

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.08042

zbMATH Keywords

period constantcritical period bifurcation\( Z_2\)-equivariant quintic systemweak bi-center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Uses Software

• Mathematica

Cites Work

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• Weak centers and bifurcation of critical periods in reversible cubic systems
• Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields
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• Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems
• Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems
• The Center and Cyclicity Problems
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• Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• Critical period bifurcations of a cubic system
• CRITICAL PERIODS OF THIRD-ORDER PLANAR HAMILTONIAN SYSTEMS

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