Controlling dynamical systems: applications to information processing and secure communications

We develop an analytic approach to a parametric (multiplicative) non-feedback method of the stabilization of the prescribed orbits of dynamical systems. On the basis of the evolved theory, a new original way of coding and secure communications is described. The foundation of this method is a ciphering by the one-to-one correspondence between periods of stabilized orbits and certain alphabet symbols. Transmission of the coded symbols is realized by sending the perturbations. Deciphering consists of the fact that the received perturbations are applied to the map which is contained in the receiver. Analytic estimations of the admissible noise level in the communication channel are given.