| Abstract: |
| We explore the connection between the complexity of a minimal subshift and the restricted orbit equivalence classes of its invariant measures. It is known that if a minimal subshift has sub-linear complexity, then all its invariant measures are Loosely Bernoulli, and therefore give rise to evenly Kakutani equivalent actions. We show that superlinear complexity, on the other hand, allows the presence of non-Loosely Bernoulli ergodic measures. In particular we construct an example of a minimal subshift which supports a Loosely Bernoulli and a non-Loosely Bernoulli invariant measure. |
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