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Uniformly recurrent sequences and minimal Cantor omega-limit sets

Lori Alvin — 2015

Fundamenta Mathematicae

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.

Adding machines, endpoints, and inverse limit spaces

Lori Alvin;  Karen Brucks — 2010

Fundamenta Mathematicae

Let f be a unimodal map in the logistic or symmetric tent family whose restriction to the omega limit set of the turning point is topologically conjugate to an adding machine. A combinatoric characterization is provided for endpoints of the inverse limit space (I,f), where I denotes the core of the map.

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