On the number of limit cycles near a homoclinic loop with a nilpotent singular point

DOI10.1016/j.jde.2015.01.006zbMath1332.34059OpenAlexW2006943190MaRDI QIDQ2350024

Yulian An, Mao'an Han

Publication date: 18 June 2015

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

Full work available at URL: https://doi.org/10.1016/j.jde.2015.01.006

zbMATH Keywords

bifurcationlimit cycleMelnikov functionintegrable systemnilpotent singular point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) 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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line ⋮ The maximal number of limit cycles bifurcating from a Hamiltonian triangle in quadratic systems ⋮ Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Limit cycles in a quartic system with a third-order nilpotent singular point ⋮ A class of quadratic reversible systems with a center of genus one ⋮ TRANSVERSE HOMOCLINIC ORBIT BIFURCATED FROM A HOMOCLINIC MANIFOLD BY THE HIGHER ORDER MELNIKOV INTEGRALS ⋮ Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field ⋮ New Double Bifurcation of Nilpotent Focus ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems

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