The early reception in France of the work of Poincaré and Lyapunov in the qualitative theory of differential equations
The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
The XVI-th Hilbert problem about limit cycles
1. Introduction. The XVI-th Hilbert problem consists of two parts. The first part concerns the real algebraic geometry and asks about the topological properties of real algebraic curves and surfaces. The second part deals with polynomial planar vector fields and asks for the number and position of limit cycles. The progress in the solution of the first part of the problem is significant. The classification of algebraic curves in the projective plane was solved for degrees less than 8. Among general...
Transformations of linear differential equations of second order and adjoined nonlinear equations