Nonlinear signals self-similarity and asymptotical estimations of ideal topological stabilization

Topological stabilization dynamics of Takens attractor is investigated when enlarging phase space dimension. The exact ideal topological stabilization is shown to be impossible for chaotic attractors, so the method of asymptotical investigation of topological changes is suggested. This method allows to reduce computer time and increase accuracy in comparison with local-topological analysis proposed previously. Numerical simulations showed the high accuracy and reliability of proposed method