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

#### 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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2013
Hamiltonian systems; global centers; global isochrony.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/614352
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