On the mean $Ψ$-intermediate dimensions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929419805786112 |
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| author | Liu, Yu Selmi, Bilel Li, Zhiming |
| author_facet | Liu, Yu Selmi, Bilel Li, Zhiming |
| contents | In this paper, we introduce the mean $Ψ$-intermediate dimension which has a value between the mean Hausdorff dimension and the metric mean dimension, and prove the equivalent definition of the mean Hausdorff dimension and the metric mean dimension. Furthermore, we delve into the core properties of the mean $Ψ$-intermediate dimensions. Additionally, we establish the mass distribution principle, a Frostman-type lemma, Hölder distortion, and derive the corresponding product formula. Finally, we provide illustrative examples of the mean $Ψ$-intermediate dimension, demonstrating its practical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the mean $Ψ$-intermediate dimensions Liu, Yu Selmi, Bilel Li, Zhiming Dynamical Systems 28A78, 28A80, 37B99 In this paper, we introduce the mean $Ψ$-intermediate dimension which has a value between the mean Hausdorff dimension and the metric mean dimension, and prove the equivalent definition of the mean Hausdorff dimension and the metric mean dimension. Furthermore, we delve into the core properties of the mean $Ψ$-intermediate dimensions. Additionally, we establish the mass distribution principle, a Frostman-type lemma, Hölder distortion, and derive the corresponding product formula. Finally, we provide illustrative examples of the mean $Ψ$-intermediate dimension, demonstrating its practical applications. |
| title | On the mean $Ψ$-intermediate dimensions |
| topic | Dynamical Systems 28A78, 28A80, 37B99 |
| url | https://arxiv.org/abs/2407.09843 |