The third order Melnikov function of a quadratic center under quadratic perturbations
Copyright policy )The third order Melnikov function of a quadratic center under quadratic perturbations
We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.
- Hebei University China (People's Republic of)
- PEKING UNIVERSITY China (People's Republic of)
- PEKING UNIVERSITY China (People's Republic of)
- Autonomous University of Barcelona Spain
- Peking University China (People's Republic of)
Bifurcation theory for ordinary differential equations, quadratic systems, Bifurcació, Teoria de la, limit cycles, Quadratic systems, Applied Mathematics, high order Melnikov functions, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Funcions, Limit cycles, High order Melnikov functions, Bifurcations of limit cycles and periodic orbits in dynamical systems, bifurcation, Bifurcation, Analysis
Bifurcation theory for ordinary differential equations, quadratic systems, Bifurcació, Teoria de la, limit cycles, Quadratic systems, Applied Mathematics, high order Melnikov functions, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Funcions, Limit cycles, High order Melnikov functions, Bifurcations of limit cycles and periodic orbits in dynamical systems, bifurcation, Bifurcation, Analysis
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