arXiv subjects

Daniel Wójcik

Publications and source records attributed to Daniel Wójcik.

2 recordsLinked to original sources

arXiv2020

On the Pappus arrangement of lines, forth and back and to the point

The purpose of this paper is to study the famous Pappus configuration of $9$ lines and its dual arrangement. We show among others that by applying the Pappus Theorem to the dual arrangement we obtain the configuration corresponding to the initial data of beginning configuration. We consider also the Pappus arrangements with some additional incidences and we establish algebraic conditions paralleling with these incidences.

math.AG↗

arXiv2000

Dimension of interaction dynamics

A method allowing to distinguish interacting from non-interacting systems based on available time series is proposed and investigated. Some facts concerning generalized Renyi dimensions that form the basis of our method are proved. We show that one can find the dimension of the part of the attractor of the system connected with interaction between its parts. We use our method to distinguish interacting from non-interacting systems on the examples of logistic and Hénon maps. A classification of all possible interaction schemes is given.

nlin.CD↗