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arXiv · 0807.0131

Isochronicity conditions for some real polynomial systems

Islam Boussaada
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Abstract

This paper focuses on isochronicity of linear center perturbed by a polynomial. Isochronicity of a linear center perturbed by a degree four and degree five polynomials is studied, several new isochronous centers are found. For homogeneous isochronous perturbations, a first integral and a linearizing change of coordinates are presented. Moreover, a family of Abel polynomial systems is also considered. By investigations until degree 10 we prove the existence of a unique isochronous center. These results are established using a computer implementation based on Urabe theorem.

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Islam Boussaada. 2008-07-01. Isochronicity conditions for some real polynomial systems. https://arxiv.org/abs/0807.0131

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