Recurrent Motions in a Piecewise Linear Oscillator

Abstract

We study the oscillator ¨x + n2x + h(x) = p(t), where h is a piecewise linear saturation function and p is a continuous 2π-periodic forcing. It is shown that there is recurrence if and only if p satisfies the Lazer–Leach condition. This condition relates the n-th Fourier coefficient of p(t) with the maximum of h and was first introduced to characterize the existence of periodic solutions.