Isochronicity conditions for some planar polynomial systems II

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 $deg(A)\le 4$ and $deg(B)\le 4$, 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.

References in corpus (1)

• A remark on rational isochronous potentials

Cited by in corpus (6)

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• Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability
• The period functions' higher order derivatives
• Renormalization group and isochronous oscillations
• A Class of Isochronous and Non-Isochronous Nonlinear Oscillators
• Complexity reduction of C-algorithm