Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-03-30
J. Phys. A: Math. Gen. 32 (1999) 1279-1283
Nonlinear Sciences
Chaotic Dynamics
8 pages
Scientific paper
10.1088/0305-4470/32/7/017
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).
Robnik Marko
Romanovski Valery G.
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