Inverse limits of Markov interval maps

Inverse limit spaces of one-dimensional continua frequently appear as attractors in dissipative dynamical systems. As such, there has been considerable interest in the topology of these inverse limit spaces. In this work we describe the topology of Markov interval maps, and use our results to show that for unimodal interval maps with finite kneading sequences, the kneading sequence and dynamics of the left endpoint determine the topology of the associated inverse limit space.