LAUSR

Abstract Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems x ˙ = P ( x , y , z ) , y ˙ = Q ( x , y , z ) , z ˙ = R ( x , y , z ) with degrees of P, Q and R equal to two when these systems have the maximum number of isolated singular points, i.e., 8 singular points. In other words we extend the well-known Berlinskii's Theorem for quadratic polynomial differential systems in the plane to the space.