A class of recursive formulas on the calculation of focus values

【摘要】 <正> Consider the problem of distinguishing between a center and a focus for the systemwhere X and Y are analytic of x and y in a neighborhood of the origin, starting withterms of degree 2, X_k and Y_k are homogeneous polynomials of degree k. The system hasa singular point of center-focus type at the origin. As is well known, one of the maindifficulties of the problem is the calculation of focus values. Based on the theory of A.M. Lyapunov and H. Poincare, two algorithms have been presented, one by finding the solu-更多还原