A Hereditarily Decomposable Generalized Inverse Limit from a Function on [0,1] with cycles of all periods

Tavish Dunn; David Ryden

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arXiv · 2209.05357

A Hereditarily Decomposable Generalized Inverse Limit from a Function on [0,1] with cycles of all periods

Tavish Dunn·David Ryden

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Abstract

In this paper, we consider inverse limits of $[0,1]$ using upper semicontinuous set-valued functions. We aim to expand on a previous paper exploring the relationship between the existence periodic points of a continuous function to the existence of indecomposable subcontinua of the corresponding inverse limit. In a previous paper, sufficient conditions were given such that if a satisfactory bonding map $F$ had a periodic cycle of period not a power of 2, then $\lim\limits_{\leftarrow}\{[0,1],F\}$ contains an indecomposable continuum. We show that the condition that $F$ is almost nonfissile is sharp by constructing an upper semicontinuous, surjective map $F$ that has the intermediate value property and periodic cycles of every period, yet produces a hereditarily decomposable inverse limit.

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Tavish Dunn, David Ryden. 2022-09-12. A Hereditarily Decomposable Generalized Inverse Limit from a Function on [0,1] with cycles of all periods. https://arxiv.org/abs/2209.05357

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