Dispersion analysis and adaptive transformation of chaotic signal attractor

The conditions of topological stabilization for Takens attractor are investigated when enlarging phase space dimension by means of dispersion analysis of topological dependences and asymptotical estimations calculation. It has been shown that ideal topological stabilization is equivalent to presence of linearized segmentation properties in time series under investigation, these properties being invariant concerning scale of partition. The exact ideal topological stabilization appears to be impossible for nonlinear time series, so we have to consider asymptotical estimations of convergence to exact stabilization. Some statistical characteristics of the investigated attractor have been defined by relative-difference investigation of obtained topological curves