Accessible points of planar embeddings of tent inverse limit spaces
Volume 541 / 2019
Dissertationes Mathematicae 541 (2019), 1-57
MSC: Primary 37B10, 37B45; Secondary 37E05, 54H20.
DOI: 10.4064/dm776-1-2019
Published online: 1 July 2019
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 the sets of accessible points and prime ends of given embeddings. We completely characterize the accessible points and prime ends of standard embeddings arising from the Barge–Martin construction of global attractors. In the other embeddings under study we find phenomena which do not occur in the standard embeddings. Furthermore, for the non-standard embeddings we prove that the shift homeomorphism cannot be extended to a planar homeomorphism.
