Isochronicity conditions for some real polynomial systems

2008/07/01 by Islam Boussaada, Boussaada, Islam
Mathematics · #34C15 #34C25 #34C37 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34C15 #msc:34C25 #msc:34C37

paper · pdf · doi:10.48550/arxiv.0807.0131

26 pages

arxiv created 2008/07/01 · arxiv updated 2009/12/01

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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