Expansions of solutions to an ODE system

We consider a system of ordinary differential equations of very general form. We show how one can find the following objects by means of algorithms of Power Geometry: (i) all power asymptotics of solutions to the system: (ii) all power-logarithmic expansions of the solutions having the power asymptotics. We present the corresponding theory and algorithms and give examples of calculations of mentioned objects for the N.Kowalevski system, describing motions of a rigid body with a fixed point. The main attention is given to explanations of the computational algorithms.