The complexity threshold for the emergence of Kakutani inequivalence
- Resource Type
- Working Paper
- Authors
- Cyr, Van; Johnson, Aimee; Kra, Bryna; Sahin, Ayse
- Source
- Subject
- Mathematics - Dynamical Systems
37B10, 68R15
- Language
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.