Graduate School of Economics and Business, University of Zagreb,
Kennedyev trg 6, 10000 Zagreb, Croatia

*e-mail:* `sonja@math.hr`

**Abstract.** 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.

**2000 Mathematics Subject Classification.**
37B10, 37B45.

**Key words and phrases.** Nonrecurrent critical point, tent map,
inverse limit, composant, folding point, folding pattern.

DOI: 10.3336/gm.42.1.03

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CrossRef