Asymptotics of solutions to the ordinary differential equations

Here we consider the general system of ordinary differential equations and propose a method for computation of all power and logarithmic asymptotics of its solutions § 1. The method is based on algorithms of Power Geometry. In § § 2–5 we apply the method to find all logarithmic asymptotics of solutions to the modified system of equations, describing motions of a rigid body with a fixed point in the case $B\ne C$, $x_0\ne 0$, $y_0=z_0=0$. The logarithmic asymptotics form 6 families: 4 with two parameters and 2 with one parameter. All them contain usual and double logarithms.