In this paper, we study the creation of zeros in a certain type of families of functions. The families studied are given by the difference of two basic functions with a translation made in the argument of one of these functions. The problem is motivated by applications in the 16th Hilbert problem and its ramifications. Here, we apply the results obtained to the study of bifurcations of critical periods in the Loud family of quadratic centers.

中文翻译：

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函数和应用翻译族中零的分叉

在本文中，我们研究了某些类型的函数族中零点的创建。所研究的科系由两个基本功能的差异给出，并在其中一个功能的论点上进行了翻译。该问题是由第16个希尔伯特问题及其后果中的应用引起的。在这里，我们将获得的结果应用到二次中心Loud族的关键时期的分叉研究中。