Let X be a compact metric space and f:X→X be continuous. The following results about the shift maps on the inverse limit spaces are proved:① The weakly almost periodic set of the shift map equals the inverse limit space of the weakly almost periodic set of f . Similar results are proved for the quasi weakly almost periodic set

uniformly almost periodic set

measure centre and minimal centre of attraction; ② f is chaotic in the sense of Schweizer and Smital on its measure centre if the shift map is chaotic in the sense of Schweizer and Smital on its measure centre.Finally

one example is given.