Chaos, periodicity, and snakelike continua

Barge, Marcy; Martin, Joe

doi:10.1090/S0002-9947-1985-0779069-7

Chaos, periodicity, and snakelike continua
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by Marcy Barge and Joe Martin

Trans. Amer. Math. Soc. 289 (1985), 355-365

DOI: https://doi.org/10.1090/S0002-9947-1985-0779069-7

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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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