Recurrent Motions in a Piecewise Linear Oscillator
MetadataShow full item record
AuthorOrtega Ríos, Rafael
Ortega, R., Schliessauf, H. Recurrent Motions in a Piecewise Linear Oscillator. Ann. Henri Poincaré (2022). [https://doi.org/10.1007/s00023-022-01217-6]
SponsorshipGerman Research Foundation (DFG) SF-B/TRR 191
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.