Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps

In this paper we examine the inverse limits generated by inverse sequences on [0, 1] with unimodal bonding maps chosen from a two-parameter family of piecewise linear continuous functions. We demonstrate techniques for analyzing the continua generated by these sequences and use these techniques to generate sufficient conditions for these sequences to give rise to indecomposable inverse limits. Interest in these inverse limit spaces arises from the fact that subcontinua of inverse limits using a single tent map as the bonding map are homeomorphic to such inverse limits. (C) 2001 Elsevier Science B.V. All rights reserved.