Linear recursion formulas of quantities of singular point and applications. (Q1415271)

The authors investigate real planar ordinary differential equations in the vicinity of singular points whose linear normal form is a center. With the use of a change of variables the system can be reduced to a normal form represented by formal power series. Based on that form the authors derive quantities which allow in principle a description of the dynamics. Moreover, recursion formulae for these quatities are proveded. Thus, the calculation can be done with computer algebra systems such as Mathematica. For polynomial planar systems up to cubic terms a complete explicit representation of these quantities is given. Finally, this process is illustrated by discussing an example.