Table 1: Closed Form Expressions For nth Iterates of (az+b)/(cz+d)

Case 1: ad = bc, c 0

Case 2: c = 0, a = d 0

Case 3: c = 0, a d

Case 4: c 0, (a-d)2 = -4bc

Case 5: c 0, (a-d)2 -4bc

where

and