BIFURCATIONS OF LIMIT CYCLES IN A Z2-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

DOI10.1142/S0218127406015210zbMath1111.37034OpenAlexW1970034488MaRDI QIDQ5484880

Mingji Zhang, Shumin Li, Ji-Bin Li

Publication date: 21 August 2006

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

Full work available at URL: https://doi.org/10.1142/s0218127406015210

zbMATH Keywords

limit cyclesbifurcationHilbert's 16th problemperturbed planar Hamiltonian systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Dynamics induced by flows and semiflows (37C10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (11)

Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 7 ⋮ New results on the study of \(Z_q\)-equivariant planar polynomial vector fields ⋮ On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ Hilbert's sixteenth problem for polynomial Liénard equations ⋮ Bifurcation of Limit Cycles in a 12-Degree Hamiltonian System Under Thirteenth-Order Perturbation ⋮ \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles ⋮ Lower bounds for the Hilbert number of polynomial systems ⋮ SMALL LIMIT CYCLES BIFURCATING FROM Z₄-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7 ⋮ ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant planar polynomial vector field of degree 7 ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems

Cites Work

• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• Some lower bounds for \(H(n)\) in Hilbert's 16th problem
• Mathematical problems for the next century
• Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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