The Theory of Bifurcations in the Work of A.A. Andronov

Abstract

“The main thing we must do with the differential equations of physical models is to investigate what is possible and what it is necessary to change in them”, said Poincaré (La valeur de la science, Part 2, Chapter V (Analysis and physics), p. 222 (1905b)). In 1931, following this prescription, A.A. Andronov (1933) came out with a vast program (also set forth in the preface to Andronov and Khajkin, 1937) which differs from the contemporary program of catastrophe theorists only in that the qualitative theory of differential equations and Poincaré’s theory of bifurcations take the place of Whitney’s theory of singularities of differentiable mappings, as yet uncreated at his time.