BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9

DOI10.1142/S0218127406016070zbMath1192.37072OpenAlexW2119299479MaRDI QIDQ3579266

Pei Yu, Ji-Bin Li, Sharon Wang

Publication date: 6 August 2010

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

Full work available at URL: https://doi.org/10.1142/s0218127406016070

zbMATH Keywords

limit cycleHamiltonian systemHilbert's 16th problemequivariant vector field

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items

Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 7 ⋮ AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A QUINTIC HAMILTONIAN PLANAR VECTOR FIELD UNDER QUINTIC PERTURBATION ⋮ Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5 ⋮ On the number of limit cycles of a \(\mathbb{Z}_4\)-equivariant quintic near-Hamiltonian system ⋮ Bifurcation of Limit Cycles in a 12-Degree Hamiltonian System Under Thirteenth-Order Perturbation ⋮ Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ 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 ⋮ On limit cycles of the Liénard equation with \(Z_2\) symmetry ⋮ AN IMPROVED LOWER BOUND ON THE NUMBER OF LIMIT CYCLES BIFURCATING FROM A HAMILTONIAN PLANAR VECTOR FIELD OF DEGREE 7 ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle

Cites Work

• Unnamed Item
• Abelian integrals and bifurcation theory
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• 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
• THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
• Essential Maple 7
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Bifurcation Theory and Methods of Dynamical Systems
• Polynomial systems: a lower bound for the Hilbert numbers
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM