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arXiv · 2206.10047

Measure-Theoretically Mixing Subshifts of Minimal Word Complexity

Darren Creutz
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Abstract

We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every superlinear $f : \mathbb{N} \to \mathbb{N}$, i.e. $f(q)/q \to \infty$, there exists a subshift admitting a (strongly) mixing of all orders probability measure with word complexity $p$ such that $p(q)/f(q) \to 0$. For a subshift with word complexity $p$ which is non-superlinear, i.e. $\liminf p(q)/q < \infty$, every ergodic probability measure is partially rigid.

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Darren Creutz. 2022-06-20. Measure-Theoretically Mixing Subshifts of Minimal Word Complexity. https://arxiv.org/abs/2206.10047

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