Countable inverse limits of postcritical \omega-limit sets of unimodal maps
Dynamical Systems
2019-03-19 v1
Abstract
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 {{\omega}(c),f| {\omega}(c) }. In this paper we consider the relationship between the limit complexity of {\omega}(c) and the limit complexity of I. We show that if {\omega}(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 {\omega}(c).
Cite
@article{arxiv.1903.07529,
title = {Countable inverse limits of postcritical \omega-limit sets of unimodal maps},
author = {Chris Good and Robin Knight and Brian Raines},
journal= {arXiv preprint arXiv:1903.07529},
year = {2019}
}