Self-Excited Oscilations : from Poincar\'e to Andronov

Abstract

In 1908 Henri Poincar\'e gave a series of 'forgotten lectures' on wireless telegraphy in which he demonstrated the existence of a stable limit cycle in the phase plane. In 1929 Aleksandr Andronov published a short note in the Comptes Rendus in which he stated that there is a correspondence between the periodic solution of self-oscillating systems and the concept of stable limit cycles introduced by Poincar\'e. In this article Jean-Marc Ginoux describes these two major contributions to the development of non-linear oscillation theory and their reception in France.