Glasnik Matematicki, Vol. 42, No.1 (2007), 43-56.

STRUCTURE OF INVERSE LIMIT SPACES OF TENT MAPS WITH NONRECURRENT CRITICAL POINTS

Brian Raines and Sonja Štimac

Department of Mathematics, Baylor University, Waco, TX, USA
e-mail: brian_raines@baylor.edu

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.


Full text (PDF) (free access)

DOI: 10.3336/gm.42.1.03


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