A study of the static and global bifurcations for Duffing equation (Q1579187)

The content of the paper is based on a well-known variant of Poincaré expansion of a solution in integer powers of a small parameter. It was already repeatedly noted in the literature, starting from von Zeipel (1916), that such variant does not permit to determine all steady states, and cannot thus serve as a basis for a systematic study of bifurcations. For a more extensive analysis of those problems see chapters 1 and 2 of the monograph by \textit{I. Gumowski} [Oscillatory evolution processes. Quantitative analysis arising from applied science. Nonlinear Science: Theory and Applications. Manchester etc.: Manchester University Press. vi (1989; Zbl 0695.34030)].