Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5

DOI10.1016/j.jmaa.2006.05.056zbMath1122.34025OpenAlexW1972909096MaRDI QIDQ864702

N. E. Zubov

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.05.056

zbMATH Keywords

Hopf bifurcationnormal formfocal value

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) 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)

Related Items (8)

Bifurcations of limit cycles in equivariant quintic planar vector fields ⋮ Limit cycles bifurcated from some \(Z_4\)-equivariant quintic near-Hamiltonian systems ⋮ SMALL LIMIT CYCLES BIFURCATING FROM Z₄-EQUIVARIANT NEAR-HAMILTONIAN SYSTEM OF DEGREES 9 AND 7 ⋮ Bifurcations of limit cycles in a \(Z_{4}\)-equivariant planar polynomial vector field of degree 7 ⋮ The number of small amplitude limit cycles in arbitrary polynomial systems ⋮ On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system ⋮ Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems

Cites Work

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• Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• Mathematical problems for the next century
• Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7
• Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
• Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
• Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
• Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 5
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations
• BIFURCATION OF LIMIT CYCLES IN Z₁₀-EQUIVARIANT VECTOR FIELDS OF DEGREE 9
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE CONTROL OF PARAMETERS OF DISTRIBUTIONS OF LIMIT CYCLES FOR A Z₂-EQUIVARIANT PERTURBED PLANAR HAMILTONIAN POLYNOMIAL VECTOR FIELD
• BIFURCATIONS OF LIMIT CYCLES IN A Z₃-EQUIVARIANT VECTOR FIELD OF DEGREE 5
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM

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