Perturbations of symmetric elliptic Hamiltonians of degree four

DOI10.1016/j.jde.2006.07.016zbMath1105.37034OpenAlexW2019584494MaRDI QIDQ859498

Chengzhi Li, Pavao Mardešić, Robert Roussarie

Publication date: 16 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.jde.2006.07.016

zbMATH Keywords

bifurcation diagramMelnikov functionsChebychev propertyunfolding symmetric Hamiltonian systems

Mathematics Subject Classification ID

Related Items (10)

Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems ⋮ Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops ⋮ Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles ⋮ Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop ⋮ Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems ⋮ Bifurcations on a five-parameter family of planar vector field ⋮ Unfolding of the Hamiltonian triangle vector field ⋮ Principal part of multi-parameter displacement functions

Cites Work

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• Abelian integrals in non-symmetric perturbation of symmetric Hamiltonian vector field
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Stability of \(C^ \infty\) mappings. III: Finitely determined map germs
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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