Abstract
An oscillator such that all motions have the same minimal period is called isochronous. When the isochronous is forced by a time-dependent perturbation with the same natural frequency as the oscillator the phenomenon of resonance can appear. This fact is well understood for the harmonic oscillator and we extend it to the nonlinear scenario.
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J. Ai, K.S. Chou, J. Wei, Self-similar solutions for the anisotropic affine curve shortening problem. Calc. Var. Partial Differ. Equations 13, 311–337 (2001)
D. Bonheure, C. Fabry, D. Smets, Periodic solutions of forced isochronous oscillators at resonance. Discrete Contin. Dyn. Syst. 8, 907–930 (2002)
R. Ortega, Periodic perturbations of an isochronous center. Qual. Theory Dyn. Syst. 3, 83–91 (2002)
R. Ortega, D. Rojas, Periodic oscillators, isochronous centers and resonance. Nonlinearity 32, 800–832 (2019)
E. Pinney, The nonlinear differential equation \(y^{\prime \prime }+p(x)y+cy^{-3}=0\). Proc. Amer. Math. Soc. 1, 681 (1950)
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Rojas, D. (2019). Resonance of Isochronous Oscillators. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_13
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DOI: https://doi.org/10.1007/978-3-030-25261-8_13
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Publisher Name: Birkhäuser, Cham
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Online ISBN: 978-3-030-25261-8
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