Free ergodic ℤ²-systems and complexity

Cyr, Van; Kra, Bryna

doi:10.1090/proc/13279

Free ergodic $\mathbb {Z}^2$-systems and complexity
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Proc. Amer. Math. Soc. 145 (2017), 1163-1173 Request permission

Abstract:

Using results relating the complexity of a two dimensional subshift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on $[0,1)$ which is invariant under both $x\mapsto px \pmod 1$ and $x\mapsto qx \pmod 1$, showing that any potential counterexample has a nontrivial lower bound on its complexity.

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