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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 $\stackrel{˙}{x}={H}_{y}+\epsilon P\left(x,y\right)$, $\stackrel{˙}{y}=-{H}_{x}+\epsilon Q\left(x,y\right)$. The authors give ane stimate on the number of limit cycles for a family of such polynomial systems.
##### MSC:
 34C07 Theory of limit cycles of polynomial and analytic vector fields 34C05 Location of integral curves, singular points, limit cycles (ODE)
limit cycle