Quantifying Poincaré's continuation method for nonlinear oscillators (Q1668937)

Summary: In the sixties, \textit{W. S. Loud} obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter [Mem. Am. Math. Soc. 47, 133 p. (1964; Zbl 0128.31802)]. In this paper Loud's results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem.