Asymptotic Dynamics Via a Time Set Without any Order

Abstract In this paper the notion of time as an algebraic object in the system theory is considered. Quasi-limit sets for semi-dynamical systems as the invariant objects under topological conjugate relations are studied. By using of the special kind of subgroups of a topological semigroup some orbits in the quasi-limit set of a topological semi-dynamical system are detected. Complete semi-dynamical systems by using of completely simple semigroups are considered. New meaning of time in hyper dynamical systems are presented.