Uncountable ω-limit sets with isolated points

Chris Good, Brian E. Raines, and Rolf Suabedissen. "Uncountable ω-limit sets with isolated points." Fundamenta Mathematicae 205.2 (2009): 179-189. <http://eudml.org/doc/283093>.

@article{ChrisGood2009,
abstract = {We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable. Secondly, we give an example of an ω-limit set of the form C ∪ R for which the Cantor set C is minimal.},
author = {Chris Good, Brian E. Raines, Rolf Suabedissen},
journal = {Fundamenta Mathematicae},
keywords = {omega limit set; limit type; attractor; invariant set; unimodal; interval map},
language = {eng},
number = {2},
pages = {179-189},
title = {Uncountable ω-limit sets with isolated points},
url = {http://eudml.org/doc/283093},
volume = {205},
year = {2009},
}

TY - JOUR
AU - Chris Good
AU - Brian E. Raines
AU - Rolf Suabedissen
TI - Uncountable ω-limit sets with isolated points
JO - Fundamenta Mathematicae
PY - 2009
VL - 205
IS - 2
SP - 179
EP - 189
AB - We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable. Secondly, we give an example of an ω-limit set of the form C ∪ R for which the Cantor set C is minimal.
LA - eng
KW - omega limit set; limit type; attractor; invariant set; unimodal; interval map
UR - http://eudml.org/doc/283093
ER -