In this paper we prove that the time part of the germ of an analytic family of vector fields with a Hopf bifurcation is rigid in the parameter. Time parts are associated with the temporal invariant of the analytic classification. Because the eigenvalues at zero are complex conjugate, time parts usually unfold in the hyperbolic direction, where the singular points are linearizable. We first identify the time part of a generic conformal family and prove that any weak holomorphic conjugacy between two time parts yields a biholomorphism analytic in the parameter. The existence of Fatou coordinates in both the Siegel and in the Poincaré domains plays a fundamental role in the proof of this result.

在本文中，我们证明了具有 Hopf 分叉的矢量场解析族的胚芽的时间部分在参数中是刚性的。时间部分与分析分类的时间不变量相关联。由于零处的特征值是复共轭，时间部分通常在双曲线方向展开，其中奇异点是可线性化的。我们首先确定通用保形族的时间部分，并证明两个时间部分之间的任何弱全纯共轭都会在参数中产生双全纯解析。在 Siegel 域和 Poincaré 域中法图坐标的存在在证明这一结果方面起着重要作用。