Topological mixing properties of rank‐one subshifts

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Article describes study examining the topological mixing properties and the maximal equicontinuous factor of rank‐one subshifts as topological dynamical systems

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21 p.

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Gao, Su & Ziegler, Caleb February 7, 2019.

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Article describes study examining the topological mixing properties and the maximal equicontinuous factor of rank‐one subshifts as topological dynamical systems

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21 p.

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Abstract: We study topological mixing properties and the maximal equicontinuous factor of rank‐one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank‐one subshift is finite. We also determine all the finite factors of a rank‐one shift with a condition involving the cutting and spacer parameters. For rank‐one subshifts with bounded spacer parameter we completely characterize weak mixing and mixing. For rank‐one subshifts with unbounded spacer parameter we prove some sufficient conditions for weak mixing and mixing. We also construct some examples showing that the characterizations for the bounded spacer parameter case do not generalize to the unbounded spacer parameter case.

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  • Transactions of the London Mathematical Society, 6(1), John Wiley & Sons, February 2019

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  • Publication Title: Transactions of the London Mathematical Society
  • Volume: 6
  • Issue: 1
  • Pages: 21
  • Peer Reviewed: Yes

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  • February 7, 2019

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  • June 16, 2020, 10:27 a.m.

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  • Feb. 8, 2021, 11:28 a.m.

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Gao, Su & Ziegler, Caleb. Topological mixing properties of rank‐one subshifts, article, February 7, 2019; (https://digital.library.unt.edu/ark:/67531/metadc1703635/: accessed May 22, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Science.

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