Structure of inverse limit spaces of tent maps with nonrecurent critical points

In this paper we examine the structure of composants of inverse limit spaces generated by tent maps with a nonrecurrent critical point. We identify important structures and substructures of certain composants, and we prove the surprising result that, assuming the critical point is nonrecurrent, there are only finitely many "types" of structures in these composants. This is an important first step towards classifying this family of inverse limit spaces which would in turn lead us closer to a proof of the Ingram Conjecture.