Abstract:

The question of the legacy of Henri Poincaré in dynamical systems has been extensively discussed during these last decades. For some authors this heritage has been difficult since it has required a total rediscovery of the seminal works of Poincaré such as his four memoirs On the curves defined by differential equations or his three volumes of New Methods of Celestial Mechanics. The aim of this work is to show, on the base of recent research, that Poincaré’s legacy has really taken place in France. It will be thus established that Poincare’s work has not been rediscovered but really continued by mathematicians such as Henry Dulac, Jacques Hadamard, Arnaud Denjoy, and also astronomers such as Jean Chazy, Pierre Fatou, Hervé Fabre. Thus, although the terrible impact produced by the First World War on French scientific community it will be also stated that a complete diffusion of Poincaré’s methods has been realized by Hadamard himself during his famous seminar at the Collège de France between 1920-1937. Then, by considering the intensive developments of the Theory of Nonlinear Oscillations by the Soviet Schools of Mandel’shtam-Papaleksi (among which is Andronov) and Kryloff-Bogoliouboff which were presented in France during this period (1929-1937) the problem of Poincaré’s legacy will appear under a new perspective.