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Global bifurcation of limit cycles in a family of polynomial systems. (English) Zbl 1050.34040
The article is devoted to one of the weakened versions of Hilbert’s 16th problem, the so-called infinitesimal Hilbert problem. This task is closely related to the problem of determining an upper bound for the number of limit cycles of the perturbed Hamiltonian system x ˙=H y +εP(x,y), y ˙=-H x +εQ(x,y). The authors give ane stimate on the number of limit cycles for a family of such polynomial systems.
MSC:
34C07Theory of limit cycles of polynomial and analytic vector fields
34C05Location of integral curves, singular points, limit cycles (ODE)
Keywords:
limit cycle