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, f λ ( x) = 4 λx(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 Feige...

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Bibliographic Details
Published in:Topology and its applications 1996, Vol.72 (2), p.159-172
Main Authors: Barge, Marcy, Ingram, W.T.
Format: Article
Language:English
Subjects:
Indecomposable continuum
Inverse limit
Logistic mapping
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Summary:In this paper we investigate inverse limits on [0, 1] using a single bonding map chosen from the logistic family, f λ ( x) = 4 λx(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.
ISSN:0166-8641
1879-3207
DOI:10.1016/0166-8641(96)00025-9