The complexity threshold for the emergence of Kakutani inequivalence

Van Cyr; Aimee Johnson; Bryna Kra; Ayşe Şahİn

doi:10.1007/s11856-022-2426-z

The complexity threshold for the emergence of Kakutani inequivalence

Van Cyr, Aimee Johnson, Bryna Kra^*, Ayşe Şahİn

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	271-300
Number of pages	30
Journal	Israel Journal of Mathematics
Volume	251
Issue number	1
DOIs	https://doi.org/10.1007/s11856-022-2426-z
State	Published - Dec 2022

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Mathematics(all)

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10.1007/s11856-022-2426-z

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title = "The complexity threshold for the emergence of Kakutani inequivalence",

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.",

author = "Van Cyr and Aimee Johnson and Bryna Kra and Ay{\c s}e {\c S}ahİn",

note = "Funding Information: The authors thank the Casa Matem{\'a}tica 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. Publisher Copyright: {\textcopyright} 2022, The Hebrew University of Jerusalem.",

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doi = "10.1007/s11856-022-2426-z",

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T1 - The complexity threshold for the emergence of Kakutani inequivalence

AU - Cyr, Van

AU - Johnson, Aimee

AU - Kra, Bryna

AU - Şahİn, Ayşe

N1 - Funding Information: 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. Publisher Copyright: © 2022, The Hebrew University of Jerusalem.

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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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JO - Israel Journal of Mathematics

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The complexity threshold for the emergence of Kakutani inequivalence

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