Ergodicity and the mixing property in the chaotic dynamics of computer systems

Abstract

Examination of the dynamics of broadly-defined computer systems that show the characteristics of a deterministic chaos requires an adjustment of the notions of ergodicity and mixing. The notions are well-defined in case of systems that range within the areas of non-zero status. The range of states of a computer system is naturally a finite set, which makes it necessary to look for differently defined dynamic characteristics that are prerequisites of chaos. The paper presents a concept of ergodicity that is construed to be a quantitative property of a computer-based dynamic system. It also discusses the problem of defining the property of mixing in the context of imminent periodicity of all the trajectories of the system.