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arXiv · 2007.09220

The complexity threshold for the emergence of Kakutani inequivalence

Van Cyr·Aimee Johnson·Bryna Kra·Ayse Sahin
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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 super-linear 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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Van Cyr, Aimee Johnson, Bryna Kra, Ayse Sahin. 2020-07-17. The complexity threshold for the emergence of Kakutani inequivalence. https://arxiv.org/abs/2007.09220

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