Global bifurcation of a perturbed double-homoclinic loop
DOI10.1007/s11401-004-0487-4zbMath1108.34039OpenAlexW2002049650MaRDI QIDQ2432007
Publication date: 24 October 2006
Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11401-004-0487-4
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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Cites Work
- Bifurcations of limit cycles forming compound eyes in the cubic system
- Global bifurcations in a perturbed cubic system with \(Z_ 2\)-symmetry
- Higher order bifurcations of limit cycles
- Cyclicity of planar homoclinic loops and quadratic integrable systems
- On the number of limit cycles in double homoclinic bifurcations
- On the cyclicity of a 2-polycycle for quadratic systems
- Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
- On the stability of double homoclinic and heteroclinic cycles.
- Bifurcation of limit cycles from a double homoclinic loop with a rough saddle
- Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
- Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles
- On the limit cycles of planar autonomous systems
- Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
- Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles
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