  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.
