Some Similar Properties Between Transitivity and Mixing

Two famous and fundamental concepts in dynamical systems are topologically transitive and topologically mixing. In this paper, we want to show that the range of every topologically transitive operator and mixing operator is dense, and also, the return set of a topologically transitive operator is an infnite subset of N, so both the return sets intopologically transitivity and mixing are infnite. Therefore, the main goal in this article is to present two similar properties between transitivity and mixing.

کلیدواژه ها:

Hypercyclicity ، Transitivity ، Mixing ، Return set