双可逆平面微分系统中心的同时性

Pub Date : 2020-12-06 DOI:10.1080/14689367.2020.1853061

J. Giné, C. Valls

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引用次数: 1

摘要

摘要给出了两类平面双可逆五次系统中心同时存在的充分条件。通过计算震源值，利用交叉结果和Gröbner基，找到了这类系统的中心条件。结果表明，在五次系统中存在一种中心数大于5的对称性，从而高于系统的度。这一事实为以前的工作中提出的问题提供了一个反例。

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Simultaneity of centres in double-reversible planar differential systems

ABSTRACT We provide the sufficient conditions for the simultaneous existence of centres for two families of planar double-reversible quintic systems. Computing the focal values and using crossed resultants and Gröbner bases, we find the centre conditions for such systems. The results obtained show that there exist a kind of symmetry where the number of centers in a quintic system is more than 5, so higher than the degree of the system. This fact gives a counterexample to the question posed in a previous work.

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