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We study the number of limit cycles that bifurcate from the periodic orbits of the center ẋ=−yR(x,y), ẏ=xR(x,y) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree n. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular...
In this paper we study the maximum number of limit cycles that can bifurcate from the period annulus surrounding the origin of a class of cubic polynomial differential systems using the averaging method. More precisely, we prove that the perturbations of the period annulus of the center located at the origin of the cubic polynomial differential system ẋ=−yf(x,y), ẏ=xf(x,y), where f(x,y)=0 is a conic...
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