Etude de cycles limites des champs de vecteurs polynômiaux par la méthode de moyennisation

Abstract

This thesis in interested to the study of the maximum number of limit cycles of ordinary differential systems depending of a small parameter. More specifically, we study two classes of differential systems using the averaging theory of first and second order. The first class studied the polynomial differentiial systems of the form dx/dt=y-∑_(l≥1)(h^l (g1l (x)+f1l (x)y)) dy/dt=-x-∑_(l≥1)(h^l (g2l (x)+f1l (x)y)), where f1l(x), g1l(x), f2l(x) and g2l(x) have degree 4 for each l= 1; 2; and h a small paramater. The second class studied the polynomial Kukles differential system of the form dx/dt=-y dy/dt=x-h(x^2+y^2 )(A-p(x,y)), where A > 0, the polynomial q(x, y) has degree n - 2 > 1 and q(0, 0) = 0.