A remark on rational isochronous potentials

Details A remark on rational isochronous potentials A remark on rational isochronous potentials

2004-09-23

arxiv.org/abs/math-ph/0409062v2

Physics

Mathematical Physics

5 pages, contribution to a special issue of JNMP dedicated to F. Calogero, slightly revised version

Scientific paper

We consider the rational potentials of the one-dimensional mechanical
systems, which have a family of periodic solutions with the same period
(isochronous potentials). We prove that up to a shift and adding a constant all
such potentials have the form $U(x) = 1/2 \omega^2 x^2$ or $U(x) = 1/8 \omega^2
x ^2 + c^2 x^{-2}.$

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