Chaos , Periodicity , and Snakelike Continua
نویسندگان
چکیده
The results of this paper relate the dynamics of a continuous map/of the interval and the topology of the inverse limit space with bonding map /. 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 / are complicated, the inverse limit space contains indecomposable subcontinua. We also establish a partial converse. Introduction. Let / be a closed interval, and let /: /-» / be a continuous function. Associated with / is the inverse limit space (/, /) = {(x0, xx,.. .)|/(* " +i) = xn}. With a natural topology, (/, /) is a compact, connected, metric space, and is an example of what Bing [Bi] has called a snakelike continuum. In this paper we will investigate the relationship between behavior of the orbits {f(x)\n ^ 0} of points of / under/, and the topological properties of the space (/,/). These examples suggest some of the ideas which we will explore.
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