Infinite topological entropy, positive mean dimension, and factors of subshifts
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916691400720384 |
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| author | Jin, Lei Qiao, Yixiao |
| author_facet | Jin, Lei Qiao, Yixiao |
| contents | We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical systems, the subshifts of block type in the Hilbert cube. This in particular leads to a large class of concrete (and new) examples of dynamical systems having this property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite topological entropy, positive mean dimension, and factors of subshifts Jin, Lei Qiao, Yixiao Dynamical Systems We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical systems, the subshifts of block type in the Hilbert cube. This in particular leads to a large class of concrete (and new) examples of dynamical systems having this property. |
| title | Infinite topological entropy, positive mean dimension, and factors of subshifts |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.11040 |