THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER CUBIC PERTURBATIONS

DOI10.1142/S0218127404010102zbMath1070.34050MaRDI QIDQ4655660

Wencheng Chen, Tonghua Zhang, Hong Zang

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

limit cycleAbelian integralHamiltonian systemweakened Hilbert's 16th problem

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (4)

ABELIAN INTEGRALS FOR THE ONE-PARAMETER BOGDANOV–TAKENS SYSTEM ⋮ ON THE NUMBER OF ZEROS OF THE ABELIAN INTEGRALS FOR A CLASS OF PERTURBED LIÉNARD SYSTEMS ⋮ Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles ⋮ The number of limit cycles for a family of polynomial systems

Cites Work

• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• Real analytic varieties with the finiteness property and complex abelian integrals
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• On Hopf cyclicity of planar systems
• Cyclicity of homoclinic loops and degenerate cubic Hamiltonians
• Perturbations of a kind of degenerate quadratic Hamiltonian system with saddle-loop
• On the number of limit cycles in double homoclinic bifurcations
• A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
• The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• On Second Order Bifurcations of Limit Cycles
• Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles
• On the limit cycles of planar autonomous systems

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