Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers

DOI10.1016/j.matcom.2017.06.002zbMath1484.37058OpenAlexW2729935009MaRDI QIDQ1996964

Fabio Scalco Dias, Claudia Valls, Jaume Llibre

Publication date: 1 March 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/199358

zbMATH Keywords

phase portraitnilpotent centerpolynomial Hamiltonian systemsPoincaré compactification

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items (7)

Unnamed Item ⋮ Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Global phase portraits and bifurcation diagrams for Hamiltonian systems of linear plus quartic homogeneous polynomials symmetric with respect to the \(y\)-axis ⋮ Global phase portraits and bifurcation diagrams for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials ⋮ Reversible polynomial Hamiltonian systems of degree 3 with nilpotent saddles ⋮ Unnamed Item ⋮ Global Phase Portraits of ℤ2-Symmetric Planar Polynomial Hamiltonian Systems of Degree Three with a Nilpotent Saddle at the Origin

Cites Work

• Uniform isochronous cubic and quartic centers: revisited
• Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Reversible nilpotent centers with cubic homogeneous nonlinearities
• Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• The center problem for a linear center perturbed by homogeneous polynomials
• Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
• Limit cycles bifurcating from a degenerate center
• Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Qualitative theory of planar differential systems
• Centers: their integrability and relations with the divergence
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