On Urabe's criteria of isochronicity
Marko Robnik, Valery G. Romanovski
Abstract
We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation 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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