Accessible points of planar embeddings of tent inverse limit spaces

2017/10/31 by Anusic, Ana, Cinc, Jernej
#37B10 #37B45 #37E05 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1710.11519

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.

Related

• Uncountably many planar embeddings of unimodal inverse limit spaces
• Accessibility of countable sets in plane embeddings of arc-like continua
• The Core Ingram Conjecture for non-recurrent critical points
• Typical path components in tent map inverse limits
• Planar Embeddings with a Globally Attracting Fixed Point