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Global Isochronous Potentials

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Abstract

We present a geometric characterization of the nonlinear smooth functions \(V:\mathbb R \rightarrow \mathbb R \) for which the origin is a global isochronous center for the scalar equation \(\ddot{x}=-V^{\prime }(x)\). We revisit Stillinger and Dorignac isochronous potentials \(V\) and show a new simple explicit family. Implicit examples are easily produced.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 208, 33100 , Udine, Italy

    Gianluca Gorni

  2. Dipartimento di Informatica, Università di Verona, strada Le Grazie 15, 37134 , Verona, Italy

    Gaetano Zampieri

Authors
  1. Gianluca Gorni
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  2. Gaetano Zampieri
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Correspondence to Gaetano Zampieri.

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Dedicated to Jorge Lewowicz for his 75th birthday.

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Gorni, G., Zampieri, G. Global Isochronous Potentials. Qual. Theory Dyn. Syst. 12, 407–416 (2013). https://doi.org/10.1007/s12346-013-0097-1

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  • DOI: https://doi.org/10.1007/s12346-013-0097-1

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