Uniformly recurrent sequences and minimal Cantor omega-limit sets
Volume 231 / 2015
Fundamenta Mathematicae 231 (2015), 273-284
MSC: Primary 37B20, 37B10; Secondary 37E05, 54H20.
DOI: 10.4064/fm231-3-3
Abstract
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.
