On the Singularities of the Planar Cubic Polynomial Differential Systems and the Euler Jacobi Formula

被引：0
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作者：
Jaume Llibre
Claudia Valls
机构：
[1] Universitat Autònoma de Barcelona,Departament de Matemàtiques
[2] Universidade de Lisboa,Departamento de Matemática, Instituto Superior Técnico
来源：
Qualitative Theory of Dynamical Systems | 2020年 / 19卷
关键词：
Euler–Jacobi formula; Singular points; Topological index; Cubic polynomial differential systems; Primary 34A05; Secondary 34C05; 37C10;
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摘要：
Using the Euler–Jacobi formula we obtain 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 nine finite singular points.
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