Ergodic theory of shift transformations

The main purpose of this note is to discuss the ergodic properties of a certain class of strictly ergodic dynamical systems which appear as subsystems of the shift dynamical system defined on the power space X = AZ, where Z is the set of all integers. We discuss only the cases when the base space A is a finite set. We are particularly interested in two examples of strictly ergodic dynamical systems which are constructed by using certain number-theoretic functions. Among other things it will be shown that there exist a continuum number of strictly ergodic dynamical systems, no two of which are spectrally isomorphic.