A new notion of dimension for dynamical systems and shift embeddability
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914533108350976 |
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| author | Meyerovitch, Tom |
| author_facet | Meyerovitch, Tom |
| contents | A dynamical system $(X,T)$ is \emph{shift embeddable} if $(X,T)$ embeds continuously and equivariantly in the shift over $[0,1]^d$ for some finite $d$. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov's mean dimension and Lebesgue covering dimension of finite orbits are not the only obstructions for shift embeddability.
We present a new notion of dimension for dynamical systems over any countable group. We show that this new notion of dimension accounts for all known obstructions for shift embeddability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13161 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new notion of dimension for dynamical systems and shift embeddability Meyerovitch, Tom Dynamical Systems 37B02 (Primary) 37B05 (Secondary) A dynamical system $(X,T)$ is \emph{shift embeddable} if $(X,T)$ embeds continuously and equivariantly in the shift over $[0,1]^d$ for some finite $d$. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov's mean dimension and Lebesgue covering dimension of finite orbits are not the only obstructions for shift embeddability. We present a new notion of dimension for dynamical systems over any countable group. We show that this new notion of dimension accounts for all known obstructions for shift embeddability. |
| title | A new notion of dimension for dynamical systems and shift embeddability |
| topic | Dynamical Systems 37B02 (Primary) 37B05 (Secondary) |
| url | https://arxiv.org/abs/2601.13161 |