LET H = {(Z) = X + IY: Y > 0} AND G = Á(Z) + 2, −1/(Z) Ñ, (Z) Î C. THIS GROUP ACTS ON THE UPPER HALF PLANE, H, AND THE ASSOCIATED QUOTIENT SURFACE IS TOPOLOGICALLY A SPHERE WITH TWO CUSPS. WE CONJUGATE THE GEODESIC FLOW ON THIS SURFACE TO A SPECIAL FLOW OVER THE SYMBOLIC SPACE OF GEOMETRIC CODES ASSOCIATED TO THIS FLOW. WE WILL SHOW THAT FOR K ³ 1, A SUBSYSTEM WITH CODES FROM (Z) \ {0, ±1, ±2, · · · , ±K{ IS A TBS. WE ALSO GIVE BOUNDS FOR THE ENTROPY OF THESE SUBSYSTEMS.