Chaos and Topologically Weakly Mixing of Shift Maps on the Inverse Limit Spaces

We prove the following results about the shift map on the inverse limit space of a compact meteric space and a sole bonding map:the shift map on inverse limit space is finite type chaotic if its sole bonding map is finite type chaotic;the shift map on inverse limit space is topologically weakly mixing if its sole bonding map is topologically weakly mixing;If (X,f) is topologically conjugate with (Y,g),then lim ←(X,f) is topologically conjugate with lim ←(Y,g).