TY - JOUR

T1 - Countable inverse limits of postcritical ω-limit sets of unimodal maps

AU - Good, C.

AU - Knight, R.

AU - Raines, B.

N1 - Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/7/1

Y1 - 2010/7/1

N2 - Let f be a unimodal map of the interval with critical point c. If the orbit of c is not dense then most points in lim←{[0,1], f} have neighborhoods that are homeomorphic with the product of a Cantor set and an open arc. The points without this property are called inhomogeneities, and the set, I, of inhomogeneities is equal to lim←{ω(c), f|}. In this paper we consider the relationship between the limit complexity of w(c) and the limit complexity of I. We show that if w(c) is more complicated than a finite collection of convergent sequences then I can have arbitrarily high limit complexity. We give a complete description of the limit complexity of I for any possible ω(c).

AB - Let f be a unimodal map of the interval with critical point c. If the orbit of c is not dense then most points in lim←{[0,1], f} have neighborhoods that are homeomorphic with the product of a Cantor set and an open arc. The points without this property are called inhomogeneities, and the set, I, of inhomogeneities is equal to lim←{ω(c), f|}. In this paper we consider the relationship between the limit complexity of w(c) and the limit complexity of I. We show that if w(c) is more complicated than a finite collection of convergent sequences then I can have arbitrarily high limit complexity. We give a complete description of the limit complexity of I for any possible ω(c).

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-77954322625&md5=ace1566fd1a1a74642e8a739c39a2843

U2 - 10.3934/dcds.2010.27.1059

DO - 10.3934/dcds.2010.27.1059

M3 - Article

AN - SCOPUS:77954322625

SN - 1078-0947

VL - 27

SP - 1059

EP - 1078

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 3

ER -