一类具有非代数极限环的Liouville可积平面微分系统

2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI) Pub Date : 2021-09-21 DOI:10.1109/ICRAMI52622.2021.9585936

Meryem Belattar, R. Cheurfa, A. Bendjeddou

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引用次数: 0

摘要

本文通过将一类九次微分系统转化为伯努利微分方程，证明了它是Liouville可积的，并准确地确定了它的第一个积分。这使我们能够证明该类允许有一个包含原点的显式非代数极限环，这里是一个非初等奇点。对于奇点，在无穷远处，该类不具有奇点。

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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On a Liouville Integrable Planar Differential System with Non-Algebraic Limit Cycle

In this paper, we prove that a class of differential system of degree nine is Liouville integrable by transforming it into a Bernoulli differential equation and we determine exactly its first integral. This allows us to show that this class admits an explicit non-algebraic limit cycle enclosing the origin, here a non-elementary singular point. For singularities, at infinity, this class does not possess singular points.

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2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI)

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