Stability and expansivity of tent map

We discuss the stability and the expansivity of the tent map f : [ 0 , 1 ] → [ 0 , 1 ] f:[0,1]→ [0,1] defined by f ( x ) = 2 min { x , 1 − x } f(x)=2min \{x,1-x\} for 0 ≤ x ≤ 1 0≤ x≤ 1 . Indeed, we show that f f is neither topologically stable nor orbit shift topologically stable nor countably-expansive but is cw-topologically stable , orbit shift cw-expansive , and orbit shift α α -persistent .