Recurrent Motions in a Piecewise Linear Oscillator
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Show full item recordAuthor
Ortega Ríos, RafaelEditorial
Birkhäuser
Date
2022-07-11Referencia bibliográfica
Ortega, R., Schliessauf, H. Recurrent Motions in a Piecewise Linear Oscillator. Ann. Henri Poincaré (2022). [https://doi.org/10.1007/s00023-022-01217-6]
Sponsorship
German Research Foundation (DFG) SF-B/TRR 191Abstract
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.