Global topological properties of homogeneous vector fields in R3

In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinity are topologically equivalent to the flows of the tangent vector field Q(T)(2L) (u is an element of S-2) On the sphere S-2, and show the theorems for the global topological classification of Q(x). They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field Q(x), and obtain the criterion for the global topological equivalence of two homogeneous vector fields.