Psi-series of quadratic vector fields on the plane (Q1365657)

The study is concerned with representations of solutions of quadratic systems on the plane. It is shown how the knowledge of psi-series provides an algorithm to compute numerically the singularities of solutions. The algorithm is illustrated by an example. The Painlevé principle is checked where all integrable quadratic systems with a linear centre at the origin are displayed at the end. The study is devoted to a result about nonexistence of an transcendent first integral of a certain type.