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Accessible points of planar embeddings of tent inverse limit spaces. (English) Zbl 1431.37012

Summary: 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.

MSC:

37B45 Continua theory in dynamics
37B10 Symbolic dynamics
37E05 Dynamical systems involving maps of the interval
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