Independence, sequence entropy and mean sensitivity for invariant measures
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910901320286208 |
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| author | Liu, Chunlin Xu, Leiye Zhang, Shuhao |
| author_facet | Liu, Chunlin Xu, Leiye Zhang, Shuhao |
| contents | We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an invariant measure is an IT tuple. Furthermore, if the acting group is amenable, we show that for an ergodic measure, the sequence entropy tuples, the mean sensitive tuples along some tempered Følner sequence, and the sensitive in the mean tuples along some tempered Følner sequence coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Independence, sequence entropy and mean sensitivity for invariant measures Liu, Chunlin Xu, Leiye Zhang, Shuhao Dynamical Systems 37A15, 37A35, 37B05 We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an invariant measure is an IT tuple. Furthermore, if the acting group is amenable, we show that for an ergodic measure, the sequence entropy tuples, the mean sensitive tuples along some tempered Følner sequence, and the sensitive in the mean tuples along some tempered Følner sequence coincide. |
| title | Independence, sequence entropy and mean sensitivity for invariant measures |
| topic | Dynamical Systems 37A15, 37A35, 37B05 |
| url | https://arxiv.org/abs/2501.08069 |