SELF-EXCITED OSCILLATIONS : from Poincare to Andronov

Jean-Marc Ginoux (1)

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819

In 1908 Henri Poincaré 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 Poincaré. In this article Jean-Marc Ginoux describes these two major contributions to the development of non-linear oscillation theory and their reception in France.

Domains: Dynamical Systems [math.DS]

Jean-Marc Ginoux. SELF-EXCITED OSCILLATIONS : from Poincare to Andronov. Nieuw Archief voor Wiskunde, 2012, Nieuw Archief voor Wiskunde, 13 (3), pp.170-177. ⟨hal-01101632v2⟩