Simultaneity of centres in double-reversible planar differential systems

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2020-12-06 DOI:10.1080/14689367.2020.1853061

J. Giné, C. Valls

引用次数: 1

Abstract

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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双可逆平面微分系统中心的同时性

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。

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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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences