On the Poincaré–Lyapunov constants and the Poincare series
For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare–Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial differential systems.