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ping mian qi ci xi tong de tuo pu deng jia wen ti
Author(s): 
Pages: 87-102
Year: Issue:  2
Journal: Acta Scientiarum Naturalium Universitatis Neimongol

Keyword:  拓扑等价性同胚映射等价类平面齐次系统予备定理拓扑分类孤立奇点定义原点;
Abstract: In this paper the problem of topological equivalence of the following differential systems be treated. Where P_m、Q_m are homogeneous polynomials of degree m, 1≤m∞. Suppose that they have no commen real factors. It shows: (1). All of homogeneous differential systems on plane may divide into two classes: one of which has "true invariant rays" and the other has no "ture invariant rays", they are not homeomorphic one another (2). The systems which have no "true invariant rays" contain only three topological equivalence classes. (3). The systems which have "true invariant rays" contain enumerrable topological equivalence classes. (4). Every two of homogeneous differential systems having no "true invariant rays" are homeomorphic each other if and only if their "type numbers" are equal. (5) Every two of homogeneous differential systems having "true invariant rays" are homeomorphic each other if and only if their "type sequences" are equivalent.
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