Symbolic computation of Lyapunov coefficients in a planar Bautin bifurcation

Often in the study the periodic orbits in dynamical systems, the computation of the Lyapunov Coeficients is needed. In this paper, the calculations of this coeficients were done via complex variable transformation in order to obtain the complex normal form for a planar Bautin bifurcation. Some examples are given in order to verify the consistency of the algorithms.
Comment: 15 pages, 22 code charts, Several Compiling Problems, Major algorithm errors