Φ-mixing and Weakly Φ-sensitivity of Shift Maps on the Inverse Limit Spaces

Let Φ be a Furstenberg family.We research the dynamic properties of the shift map on the inverse limit space of a compact metric space and a sole bonding map.The following results are proved:the shift map on inverse limit space is Φ-transitive if and only if its sole bonding map is Φ-transitive;the shift map on inverse limit space is Φ-mixing if and only if its sole bonding map is Φ-mixing,where Φ is a full Furstenberg family;the shift map on inverse limit space is weakly Φ-sensitive if and only if its sole bonding map is weakly Φ-sensitive.