Inverse limits on [0,1] using logistic bonding maps

In this paper we investigate inverse limits on [0, 1] using a single bonding map chosen from the logistic family, fλ (x) = 4λx(1 − x) for 0 ⩽ λ ⩽ 1. Many interesting continua occur as such inverse limits from arcs to indecomposable continua. Among other things we observe that up through the Feigenbaum limit the inverse limit is a point or is hereditarily decomposable and otherwise the inverse limit contains an indecomposable continuum.