Stability of trajectories from Poincaré to Birkhoff: approaching a qualitative definition (Q540717)

During the 1880s, Henri Poincaré developed a qualitative approach to the study of solutions of differential equations. In this article the author studies the subsequent evolution of the concept and the meaning of the word ``qualitative'' in this connection. In particular, she discusses Birkhoff's criticism of Poincare's definition, sketches the contributions of Lyapunov and Levi-Civita, and proposes ``a clear criterion for distinguishing qualitative and quantitative approaches to stability''. The clearly written article is complemented by an extensive list of references.