Alien limit cycles near a Hamiltonian 2-saddle cycle

DOI10.1016/j.crma.2005.03.009zbMath1083.34025OpenAlexW2000206132WikidataQ114952403 ScholiaQ114952403MaRDI QIDQ1780707

Freddy Dumortier, Magdalena Caubergh, Robert Roussarie

Publication date: 13 June 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.03.009

zbMATH Keywords

limit cycleAbelian integralHamiltonian 2-saddle cyclesmooth planar vector field

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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (11)

Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems ⋮ Tangential center problem for a family of non-generic Hamiltonians ⋮ On the Number of Limit Cycles Bifurcating from a Compound Polycycle ⋮ Limit cycles appearing from a generalized heteroclinic loop with a cusp and a nilpotent saddle ⋮ PERIODIC ORBIT OF THE PENDULUM WITH A SMALL NONLINEAR DAMPING ⋮ Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop ⋮ Global bifurcation studies of a cubic Liénard system ⋮ Abelian integrals and limit cycles ⋮ Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case ⋮ BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles

Cites Work

• Unnamed Item
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Abelian integrals and limit cycles

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