A remark on rational isochronous potentials
O. A. Chalykh, A. P. Veselov
Abstract
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 ω2 x2 or U(x) = 1/8 ω2 x 2 + c2 x-2.
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