Chaos, periodicity, and snakelike continua

Abstract

The results of this paper relate the dynamics of a continuous map f f of the interval and the topology of the inverse limit space with bonding map f 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 f are complicated, the inverse limit space contains indecomposable subcontinua. We also establish a partial converse.