In this paper we aim to use different metrics in the Euclidean space and Sobolev type metrics in function spaces in order to produce reliable parameters for the differentiation of point distributions and dynamical systems. The main tool is the analysis of the geometrical evolution of the hypergraphs generated by the growth of the radial parameters for a choice of an appropriate metric in the space containing the data points. Once this geometric dynamics is obtained we use Lebesque and Sobolev type norms in order to compare the basic geometric signals obtained.

翻译：在本文中,我们的目标是在功能空间的Euclidean空间和Sobolev类型测量中使用不同的测量尺度,以便产生用于区分点分布和动态系统的可靠参数,主要工具是分析由于辐射参数增长而产生的高音的几何进化,以便在包含数据点的空间中选择适当的测量尺度。一旦获得这一几何动态,我们将使用 Lebesque 和 Sobolev 类型规范来比较所获得的基本几何信号。