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arXiv · 1602.03439

Free ergodic $\mathbb{Z}^2$-systems and complexity

Van Cyr·Bryna Kra
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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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Van Cyr, Bryna Kra. 2016-02-10. Free ergodic $\mathbb{Z}^2$-systems and complexity. https://arxiv.org/abs/1602.03439

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