On the cubic perturbations of the symmetric 8-loop Hamiltonian

DOI10.1016/J.JDE.2020.03.003zbMath1443.34040arXiv1909.09840OpenAlexW3010053896MaRDI QIDQ2180584

Iliya D. Iliev, Chengzhi Li, Jiang Yu

Publication date: 14 May 2020

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

Full work available at URL: https://arxiv.org/abs/1909.09840

zbMATH Keywords

bifurcation of limit cyclesabelian integralcyclicity of period annulihigh-order Melnikov functionsperturbation of symmetric Hamiltonian

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (4)

The limit cycles in a generalized Rayleigh-Liénard oscillator ⋮ Melnikov analysis in a cubic system with a multiple line of critical points ⋮ Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian ⋮ Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis

Cites Work

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• Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
• Higher order bifurcations of limit cycles
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields
• Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop
• Successive derivatives of a first return map, application to the study of quadratic vector fields

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