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On Urabe's criteria of isochronicity

Marko Robnik·Valery G. Romanovski
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Abstract

We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation $\ddot{x}+g(x)=0$. We show that apart from the harmonic oscillator there exists a large family of isochronous potentials which must all be non-polynomial and not symmetric (an even function of the coordinate x).

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Marko Robnik, Valery G. Romanovski. 2000-03-30. On Urabe's criteria of isochronicity. https://doi.org/10.1088/0305-4470%2F32%2F7%2F017

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