Asymptotic arc-components of unimodal inverse limit spaces

We consider the inverse limit space ( I , f ) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then ( I , f ) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].