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. © 1996 Elsevier Science B.V. All rights reserved.
M. Barge and W. T. Ingram, "Inverse Limits On [0,1] Using Logistic Bonding Maps," Topology and its Applications, vol. 72, no. 2, pp. 159 - 172, Elsevier, Jan 1996.
The definitive version is available at https://doi.org/10.1016/0166-8641(96)00025-9
Mathematics and Statistics
Keywords and Phrases
Indecomposable continuum; Inverse limit; Logistic mapping
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 1996