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Poincar\\'e in 1880's is concerned on the characterization of planar polynomial vector fields $X=(-y+P(x,y))\\dfrac{\\partial}{\\partial x}+(x+Q(x,y))\\dfrac{\\partial}{\\partial y},$ with $P(0,0)=Q(0,0)=0,$ such that all their integral trajectories are closed curves whose interiors contain a fixed point called center or such that all their integral trajectories are spirals called foci. 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