\(Z_2\)-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields

DOI10.1016/j.jde.2019.12.020zbMath1471.37056OpenAlexW2998766904MaRDI QIDQ1986526

Shimin Li, Ting Chen, Jaume Llibre

Publication date: 8 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2019.12.020

zbMATH Keywords

Hamiltonian systemphase portraitbi-center\(Z_2\)-equivariant

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Equivariant dynamical systems (37C81)

Related Items (7)

Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field ⋮ Nilpotent bi-center in continuous piecewise \(\mathbb{Z}_2\)-equivariant cubic polynomial Hamiltonian systems ⋮ On the indices of singular points for planar bounded piecewise smooth polynomial vector field ⋮ Double homoclinic bifurcations by perturbing a class of cubic \(\mathrm{Z}_2\)-equivariant polynomial systems with nilpotent singular points ⋮ Complete classification on center of cubic planar systems symmetric with respect to a straight line ⋮ Phase portraits and bifurcation diagram of the Gray-Scott model ⋮ Isochronicity of bi-centers for symmetric quartic differential systems

Cites Work

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• New results on the study of \(Z_q\)-equivariant planar polynomial vector fields
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• Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
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• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Qualitative theory of planar differential systems
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• Classification of Continuous Flows on 2-Manifolds
• Local analytic integrability for nilpotent centers
• Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• A SURVEY ON THE BLOW UP TECHNIQUE
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
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