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 H\'enon maps. A classification of all possible interaction schemes is given.