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Uniformly recurrent sequences and minimal Cantor omega-limit sets

Volume 231 / 2015

Lori Alvin 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.

Authors

  • Lori AlvinDepartment of Mathematics
    Bradley University
    1501 W. Bradley Ave.
    Peoria, IL 61625, U.S.A.
    e-mail

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