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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.10047 |
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| _version_ | 1866917003570184192 |
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| author | Creutz, Darren |
| author_facet | Creutz, Darren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10047 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Measure-Theoretically Mixing Subshifts of Minimal Word Complexity Creutz, Darren Dynamical Systems 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. |
| title | Measure-Theoretically Mixing Subshifts of Minimal Word Complexity |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2206.10047 |