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Limit cycles bifurcating from a perturbed quartic center. (English) Zbl 1231.34057

The paper is devoted to the study of the maximum number σ of limit cycles for the differential systems

x ˙=-y(x+a)(y+b)(x+c)+εP n (x,y),y ˙=x(x+a)(y+b)(x+c)+εQ n (x,y),

bifurcating from the period annulus surrounding the origin of the unperturbed system, where a,b,c{0}, P n and Q n are real polynomials of degree n, ε is a small real parameter. By using the averaging theory of first order it is proved that 4[(n-1)/2]+4σ5[(n-1)/2]+14.

MSC:
34C07Theory of limit cycles of polynomial and analytic vector fields
34C05Location of integral curves, singular points, limit cycles (ODE)
34C23Bifurcation (ODE)
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