English

On Urabe's criteria of isochronicity

Chaotic Dynamics 2009-10-31 v1 Exactly Solvable and Integrable Systems

Abstract

We give a short proof of Urabe's criteria for the isochronicity of periodical solutions of the equation x¨+g(x)=0\ddot{x}+g(x)=0. We show that apart from the harmonic oscillator there exists a large family of isochronous potentials which must all be non-polynomial and not symmetric (an even function of the coordinate x).

Keywords

Cite

@article{arxiv.nlin/0003065,
  title  = {On Urabe's criteria of isochronicity},
  author = {Marko Robnik and Valery G. Romanovski},
  journal= {arXiv preprint arXiv:nlin/0003065},
  year   = {2009}
}

Comments

8 pages