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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 $\sigma$ of limit cycles for the differential systems $$ \dot{x}=-y(x+a)(y+b)(x+c) + \varepsilon P_n(x,y), \ \dot{y}=x (x+a)(y+b)(x+c) + \varepsilon Q_n(x,y), $$ bifurcating from the period annulus surrounding the origin of the unperturbed system, where $a,b,c\in \bbfR\setminus \{0\}$, $P_n$ and $Q_n$ are real polynomials of degree $n$, $\varepsilon$ is a small real parameter. By using the averaging theory of first order it is proved that $4[(n-1)/2]+4\leq \sigma \leq 5[(n-1)/2]+14$.

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