Accessible points of planar embeddings of tent inverse limit spaces

TL;DR

This paper investigates the accessible points and prime ends of planar embeddings of tent inverse limit spaces, introducing new techniques based on kneading theory to characterize these features in standard and non-standard embeddings.

Contribution

It provides a complete characterization of accessible points and prime ends in standard embeddings and reveals new phenomena in non-extendable embeddings.

Findings

Complete characterization of accessible points in standard embeddings

Identification of new phenomena in non-extendable embeddings

Application of kneading theory to topological properties of inverse limit spaces

Abstract

In this paper we study a class of embeddings of tent inverse limit spaces. We introduce techniques relying on the Milnor-Thurston kneading theory and use them to study sets of accessible points and prime ends of given embeddings. We completely characterize accessible points and prime ends of standard embeddings arising from the Barge-Martin construction of global attractors. In other (non-extendable) embeddings we find phenomena which do not occur in the standard embeddings.