Published online by Cambridge University Press: 22 January 2016
We have given in [3] the definition of the quasi-flow and discussed the representation and the time-change of the quasi-flow. Further we have defined the TQ-system and studied some properties of them using the time-change and the representation of the quasi-flow. These properties are very useful to study the ergodicity, the entropy and increasing partitions of the automorphism. We are now going to extend the definition of the TQ-system and to study the similar problems as the above.