We prove that a map f is chain mixing if and only if $$f^r\times f^s$$fr×fs is chain transitive for some positive integers r, s. We prove that a map which has… Click to show full abstract
We prove that a map f is chain mixing if and only if $$f^r\times f^s$$fr×fs is chain transitive for some positive integers r, s. We prove that a map which has the average shadowing property with dense $$\underline{0}$$0̲-recurrent points is transitive, and by this result we point out that a map is multi-transitive if it has the average shadowing property and an invariant Borel probability measure with full support. Moreover, we show that $$\Delta $$Δ-mixing, the completely uniform positive entropy and the average shadowing property are equivalent mutually for a surjective map which has the shadowing property.
Journal Title: Bulletin of the Iranian Mathematical Society
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!