In Strżyna E and Żołądek H (2015 Moscow Math. J. 15 141) a complete formal normal forms for germs of two-dimensional holomorphic vector fields with nilpotent singularity was obtained. That classification is quite nontrivial (7 cases), but it can be divided into general types like in the case of the elementary singularities. One could expect that also the analytic properties of the normal forms for the nilpotent singularities are analogous to the case of the elementary singularities. This is really true. In the cases analogous to the focus and the node the normal form is analytic. In the case analogous to the nonresonant saddle the normal form is often nonanalytic due to the small divisors phenomenon. In the cases analogous to the resonant saddles (including saddle-nodes) the normal form is nonanalytic due to bad properties of some homological operators associated with the first nontrivial term in the orbital normal form.

在 Strżyna E 和 Żołądek H（2015莫斯科数学 J. 15141) 得到了具有幂零奇点的二维全纯向量场胚芽的完整形式范式。这种分类非常重要（7 种情况），但它可以分为一般类型，如基本奇点的情况。可以预料，幂零奇点的范式的解析性质也类似于基本奇点的情况。这是真的。在类似于焦点和节点的情况下，范式是解析式的。在类似于非共振鞍座的情况下，由于小除数现象，范式通常是非解析的。