Abstract In this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters. Here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used. The principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm, the so-called Roussarie-Ecalle compensator. Especial attention is paid to the remainder's properties concerning the derivation with respect to the unfolding parameters.

中文翻译：

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Dulac 映射的渐近展开和双曲鞍座展开的时间：局部设置

摘要 在本文中，我们研究了双曲共振鞍座附近平面矢量场的展开。我们给出了局部 Dulac 时间（以及局部 Dulac 映射）的渐近扩展的结构定理，其余部分关于展开参数均匀平坦。这里局部意味着足够接近鞍座，以便可以使用由合适的正常形式提供的归一化坐标。渐近展开的主要部分以包含对数变形的单项式标度给出，即所谓的 Roussarie-Ecalle 补偿器。特别注意关于展开参数推导的余数属性。