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) = 1/2ω2x2 or U(x) = ω2x2 + c2x-2.
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CITATION STYLE
APA
Chalykh, O. A., & Veselov, A. P. (2005). A remark on rational isochronous potentials. Journal of Nonlinear Mathematical Physics, 12(SUPPL. 1), 179–183. https://doi.org/10.2991/jnmp.2005.12.s1.15
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