改进的Euler–Jacobi公式和中的平面三次多项式向量场ℝ2.

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED Dynamical Systems-An International Journal Pub Date : 2022-04-21 DOI:10.1080/14689367.2022.2066508

J. Llibre, C. Valls

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引用次数: 1

摘要

多重数为2的点的新Euler–Jacobi公式提供了多项式向量场的奇异点与其拓扑指数之间的代数关系。利用这个公式，我们得到了平面三次多项式微分系统的奇异点的配置及其拓扑指数，当这些系统有八个有限奇异点时，这些奇异点是其中一个重数为2的奇异点。使用经典的Euler–Jacobi公式已经解决了具有九个有限奇异点的情况。

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The improved Euler–Jacobi formula and the planar cubic polynomial vector fields in ℝ2

The new Euler–Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. The case with nine finite singular points has already been solved using the classical Euler–Jacobi formula.

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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