We investigate the structure of kneading sequences that belong to unimodal maps for which the omega-limit set of the turning point is a minimal Cantor set. We define a scheme that can be used to generate uniformly recurrent and regularly recurrent infinite sequences over a finite alphabet. It is then shown that if the kneading sequence of a unimodal map can be generated from one of these schemes, then the omega-limit set of the turning point must be a minimal Cantor set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-3,
author = {Lori Alvin},
title = {Uniformly recurrent sequences and minimal Cantor omega-limit sets},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {273-284},
zbl = {06481155},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-3}
}
Lori Alvin. Uniformly recurrent sequences and minimal Cantor omega-limit sets. Fundamenta Mathematicae, Tome 228 (2015) pp. 273-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-3/