The complexity threshold for the emergence of Kakutani inequivalence

Van Cyr, Aimee Johnson, Bryna Kra, Ayse Sahin

Published 2020-07-17Version 1

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.