Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop

DOI10.5565/PUBLMAT_44100_08zbMath0962.34026MaRDI QIDQ1580322

Yulin Zhao, Zhi-Fen Zhang

Publication date: 14 June 2001

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/41390

zbMATH Keywords

limit cyclesHilbert's 16th problemcubic Hamiltonian systems

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

The loop quantities and bifurcations of homoclinic loops ⋮ Limit cycles of cubic polynomial vector fields via the averaging theory ⋮ Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop ⋮ Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment ⋮ Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics ⋮ Perturbations of a kind of degenerate quadratic Hamiltonian system with saddle-loop

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