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arXiv · 1005.5048

Isochronicity conditions for some planar polynomial systems II

Magali Bardet·Islam Boussaada·A. Raouf Chouikha·Jean-Marie Strelcyn
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Abstract

We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $$\dot x=-y+A(x,y),\;\dot y=x+B(x,y),$$ where $A,\;B\in \mathbb{R}[x,y]$, which can be reduced to the Liénard type equation. When $deg(A)\leq 4$ and $deg(B) \leq 4$, using the so-called C-algorithm we found $36$ new families of isochronous centers. When the Urabe function $h=0$ we provide an explicit general formula for linearization. This paper is a direct continuation of \cite{BoussaadaChouikhaStrelcyn2010} but can be read independantly.

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Magali Bardet, Islam Boussaada, A. Raouf Chouikha, Jean-Marie Strelcyn. 2010-11-05. Isochronicity conditions for some planar polynomial systems II. https://doi.org/10.1016/j.bulsci.2010.12.003

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