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The concept of "limit cycle" was introduced by Henri Poincar\'e in his secondmemoir "On curves defined by a differential equation" in 1882. From the pointof view of physics, a stable limit cycle (or attractive) is the representationof the periodic solution of a (mechanical or electrical) dissipative systemwhose oscillations are maintained by the system itself. Conversely, theexistence of a stable limit cycle ensures the maintenance of the oscillations.So far, the historiography considered that the Russian mathematician AleksandrAndronov was the first to establish such a correspondence between the periodicsolution of a self-oscillating system and Poincar\'e's concept of limit cycle.The recent discovery of a series of lectures given by Henri Poincar\'e in 1908at the School of Post and Telegraph (now Telecom Paris Tech) proves that he hadalready used his limit cycle concept to establish the existence of a regime ofmaintained waves in a wireless device of radiotechnics. This article aims onthe one hand to trace the emergence of this concept since its creation byPoincar\'e and the other hand to highlight its importance and role in thehistory of non-linear oscillations.

Henri Poincar\'e et l'\'emergence du concept de cycle limite