Embedding information onto a dynamical system

The celebrated Takens' embedding theorem concerns an attractor of a dynamical system in Euclidean space appropriate dimension through generic delay-observation map. also establishes topological conjugacy. In this paper, we show how arbitrary sequence can be mapped into another as attractive solution nonautonomous system. Such mapping entails conjugacy and between the spaces. This result is not generalization Takens but helps us understand what exactly required by discrete-time state models widely used applications to embed external stimulus onto its space. Our results settle basic problem concerning perturbation autonomous We describe happens dynamics when exogenous noise perturbs continuously local irreducible attracting set (such stable fixed point)