Unfolding of a quadratic integrable system with a homoclinic loop

DOI10.1007/s10114-002-0196-4zbMath1027.37037OpenAlexW2314418952MaRDI QIDQ1565991

Linping Peng

Publication date: 14 January 2004

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-002-0196-4

zbMATH Keywords

limit cyclesbifurcationperturbationshomoclinic loopunfoldingPoincaré transformationzeros of Abelian integralsquadratic integrable system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) 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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (10)

Studies of the Petrov module for a family of generalized Liénard integrable systems ⋮ The local period function for Hamiltonian systems with applications ⋮ The cyclicity of a class of quadratic reversible centers defining elliptic curves ⋮ The cyclicity of period annuli of a class of quadratic reversible systems with two centers ⋮ Bounding the number of zeros of certain abelian integrals ⋮ Quadratic perturbations of a quadratic reversible center of genus one ⋮ On the limit cycles bifurcating from a quadratic reversible center of genus one ⋮ FOUR LIMIT CYCLES FROM PERTURBING QUADRATIC INTEGRABLE SYSTEMS BY QUADRATIC POLYNOMIALS ⋮ Abelian integrals and limit cycles ⋮ A Chebyshev criterion for Abelian integrals

Cites Work

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• Quadratic systems with center and their perturbations
• On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
• Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops
• On the number of limit cycles arising from perturbations of homoclinic loops of quadratic integrable systems
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems

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