On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems

[摘要] Using the Euler-Jacobi formula there is a 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 polynomial differential systems (x)over dot = P(x, y, z), (y)over dot = Q(x, y, z), (z)over dot = R(x, y, z) with degrees of P, Q and R equal to two when these systems have the maximum number of isolated singular points, i.e., 8 singular points. In other words we extend the well-known Berlinskii's Theorem for quadratic polynomial differential systems in the plane to the space. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-05

[关键词] Euler-Jacobi formula;Singular points;Topological index;Polynomial differential systems;Berlinskii's Theorem