We investigate the problem of distinguishing between a centre and a focus in the class of analytic vector fields with fixed Newton diagram, which satisfy certain natural conditions of general position. A method is proposed for constructing explicit expressions for the coefficients in the asymptotic representation of the monodromy transformation, known as the Dulac series. These are analogous to the Lyapunov focal quantities. These coefficients make it possible — up to an infinite-codimensional set of exceptional cases — to complete the stability analysis for a compound monodromic (that is, centre-focus) singular point. A computer-aided calculation of formulae for coefficients of the Dulac series is presented. Examples are treated of Newton diagrams with two and three edges.

Bibliography: 30 titles.

我们研究固定牛顿图的解析矢量场类中满足中心位置某些自然条件的中心和焦点之间的区分问题。提出了一种用于构造单峰变换的渐近表示中的系数的显式表达式的方法，称为Dulac级数。这些类似于李雅普诺夫定焦量。这些系数使得-可以在一组无限维的特殊情况下-完成复合单峰（即中心焦点）奇异点的稳定性分析。提出了计算机辅助计算Dulac级数系数的公式。实例处理具有两个和三个边的牛顿图。

参考书目：30种。