Uniformly recurrent sequences and minimal Cantor omega-limit sets. (English) Zbl 1356.37025
Summary: 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.
MSC:
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37B10 | Symbolic dynamics |
| 37E05 | Dynamical systems involving maps of the interval |
| 54H20 | Topological dynamics (MSC2010) |
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