We present a geometric characterization of the nonlinear smooth functions $V:\R\to \R$ for which the origin is a global isochronous center for the scalar equation $\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials $V$ and show a new simple explicit family. Implicit examples are easily produced.
Global Isochronous Potentials
ZAMPIERI, Gaetano
2013-01-01
Abstract
We present a geometric characterization of the nonlinear smooth functions $V:\R\to \R$ for which the origin is a global isochronous center for the scalar equation $\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials $V$ and show a new simple explicit family. Implicit examples are easily produced.
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