Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914787443605504 |
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| author | Creutz, Darren |
| author_facet | Creutz, Darren |
| contents | We exhibit subshifts admitting weakly mixing (probability) measures, for arbitrary $ε> 0$, with word complexity $p$ satisfying $\limsup \frac{p(q)}{q} < 1.5 + ε$. For arbitrary $f(q) \to \infty$, said subshifts can be made to satisfy $p(q) < q + f(q)$ infinitely often.
We establish that every subshift associated to a rank-one transformation (on a probability space) which is not an odometer satisfies $\limsup p(q) - 1.5q = \infty$ and that this is optimal for rank-ones. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_08691 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts Creutz, Darren Dynamical Systems Primary: 37B10, Secondary 37A25 We exhibit subshifts admitting weakly mixing (probability) measures, for arbitrary $ε> 0$, with word complexity $p$ satisfying $\limsup \frac{p(q)}{q} < 1.5 + ε$. For arbitrary $f(q) \to \infty$, said subshifts can be made to satisfy $p(q) < q + f(q)$ infinitely often. We establish that every subshift associated to a rank-one transformation (on a probability space) which is not an odometer satisfies $\limsup p(q) - 1.5q = \infty$ and that this is optimal for rank-ones. |
| title | Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts |
| topic | Dynamical Systems Primary: 37B10, Secondary 37A25 |
| url | https://arxiv.org/abs/2205.08691 |