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The complexity threshold for the emergence of Kakutani inequivalence

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Abstract

We show that linear complexity is the threshold for the emergence of Kakutani inequivalence for measurable systems supported on a minimal subshift. In particular, we show that there are minimal subshifts of arbitrarily low superlinear complexity that admit both loosely Bernoulli and non-loosely Bernoulli ergodic measures and that no minimal subshift with linear complexity can admit inequivalent measures.

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Authors and Affiliations

  1. Department of Mathematics, Bucknell University, Lewisburg, PA, 17837, USA

    Van Cyr

  2. Departmet of Mathematics and Statistics, Swarthmore College, Swarthmore, PA, 19081, USA

    Aimee Johnson

  3. Department of Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Bryna Kra

  4. Departmet of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA

    Ayşe Şahİn

Authors
  1. Van Cyr
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  2. Aimee Johnson
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  3. Bryna Kra
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  4. Ayşe Şahİn
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Corresponding author

Correspondence to Bryna Kra.

Additional information

We dedicate this paper to Benjy Weiss on the occasion of his 80 th birthday

The authors thank the Casa Matemática Oaxaca (CMO) for hosting the “Symbolic Dynamical Systems” workshop during which this work was started. The third author was partially supported by NSF grant DMS-1800544.

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Cyr, V., Johnson, A., Kra, B. et al. The complexity threshold for the emergence of Kakutani inequivalence. Isr. J. Math. 251, 271–300 (2022). https://doi.org/10.1007/s11856-022-2426-z

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  • DOI: https://doi.org/10.1007/s11856-022-2426-z

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