Problem of invariance for discrete stabilization systems operating in conditions of regular chaos

New models of maps oriented to the solution of invariance problems in discrete dynamic systems that operate in conditions of deterministic chaos are proposed. The idea of K(E) transformation for quasi-stochastic sequences is developed based on these maps. The result is a method for the synthesis of discrete stabilization systems; this method, in combination with the principles of the classical theory of random processes, provides compensation for deterministic chaos and optimal filtering of stationary random noise.