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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Chaos, periodicity, and snakelike continua


Authors: Marcy Barge and Joe Martin
Journal: Trans. Amer. Math. Soc. 289 (1985), 355-365
MSC: Primary 58F08; Secondary 54F20, 54H20, 58F20
MathSciNet review: 779069
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Abstract: The results of this paper relate the dynamics of a continuous map $ f$ of the interval and the topology of the inverse limit space with bonding map $ f$. These inverse limit spaces have been studied by many authors, and are examples of what Bing has called "snakelike continua". Roughly speaking, we show that when the dynamics of $ f$ are complicated, the inverse limit space contains indecomposable subcontinua. We also establish a partial converse.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0779069-7
Article copyright: © Copyright 1985 American Mathematical Society