Using Melnikov functions of any order for studying limit cycles

DOI10.1016/j.jmaa.2016.11.021zbMath1367.34032OpenAlexW2549194852MaRDI QIDQ2374237

Gheorghe Tigan

Publication date: 14 December 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.11.021

zbMATH Keywords

limit cyclesHamiltonian systemsMelnikov functions

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, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (7)

The third order Melnikov function of a cubic integrable system under quadratic perturbations ⋮ On the uniqueness of limit cycles for generalized Liénard systems ⋮ Higher order Melnikov functions for studying limit cycles of some perturbed elliptic Hamiltonian vector fields ⋮ MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS FOR A CLASS OF SYMMETRIC HYPERELLIPTIC HAMILTONIAN SYSTEMS ⋮ The number of limit cycles from a cubic center by the Melnikov function of any order ⋮ A class of reversible quadratic systems with piecewise polynomial perturbations ⋮ The center conditions for a perturbed cubic center via the fourth-order Melnikov function

Cites Work

• The third order Melnikov function of a quadratic center under quadratic perturbations
• High order Melnikov functions and the problem of uniformity in global bifurcation
• Configurations of limit cycles and planar polynomial vector fields.
• A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• On Second Order Bifurcations of Limit Cycles
• Successive derivatives of a first return map, application to the study of quadratic vector fields
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