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Poincare's forgotten conferences on wireless telegraphy

At the beginning of the twentieth century while Henri Poincaré (1854-1912) was already deeply involved in the developments of wireless telegraphy, he was invited, in 1908, to give a series of lectures at the École Supérieure des Postes et Télégraphes (today Sup'Télecom). In the last part of his presentation he established that the necessary condition for the existence of a stable regime of maintained oscillations in a device of radio engineering completely analogous to the triode: the singing arc, is the presence in the phase plane of stable limit cycle. The aim of this work is to prove that the correspondence highlighted by Andronov between the periodic solution of a non-linear second order differential equation and Poincaré's concept of limit cycle has been carried out by Poincaré himself, twenty years before in these forgotten conferences of 1908.