一步摄动齐次退化中心极限环数的估计

Q3 Mathematics Extracta Mathematicae Pub Date : 2023-06-01 DOI:10.17398/2605-5686.38.1.85

Extracta Mathematicae Volumen, M. MolaeiDerakhtenjani, O. RabieiMotlagh, H. Mohammadinejad

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引用次数: 0

摘要

我们考虑一个阶为2m + 1的齐次退化中心，并用一个阶为2m的齐次多项式来扰动它。我们研究了原点周围的李雅普诺夫常数来估计极限环的数目。为此，我们对参数进行了分类，并研究了它们对极限环数的影响。最后，我们发现在没有任何条件的情况下，扰动简并中心至少有两个极限环，并且分叉极限环的个数可以达到2m + 3。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers

We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles. To do it, we classify the parameters and study their effect on the number of limit cycles. Finally, we find that the perturbed degenerate center without any condition has at least two limit cycles, and the number of the bifurcated limit cycles could reach 2m + 3.

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