ABSTRACT
This chapter aims to study the behavior of integral curves for a system of ordinary differential equations in a neighborhood of a singular point with coordinates. A result from Perron’s paper, as well as mine, makes it possible to give a geometric picture of the behavior of the trajectories near a singular point, provided that the matrix has only elementary divisors of degree 1 and, in addition, all its characteristic roots have mutually distinct real parts. The results obtained by Perron in other cases are weaker than mine and yield no precise geometric picture of the behavior of the trajectories near a singular point. It should be observed, however, that some important properties of linear systems cannot be further extended to the general case.
