A Remark on Rational Isochronous Potentials
Abstract
We consider the rational potentials of the onedimensional 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 $U(x) = 1/8 \omega^2 x ^2 + c^2 x^{2}.$
 Publication:

Journal of Nonlinear Mathematical Physics
 Pub Date:
 2005
 DOI:
 10.2991/jnmp.2005.12.s1.15
 arXiv:
 arXiv:mathph/0409062
 Bibcode:
 2005JNMP...12S.179C
 Keywords:

 Mathematical Physics;
 70H12
 EPrint:
 5 pages, contribution to a special issue of JNMP dedicated to F. Calogero, slightly revised version