Critical values for Intermediate and Box dimension of projections and other images
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912715709087744 |
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| author | Angelini, Nicolas Molter, Ursula |
| author_facet | Angelini, Nicolas Molter, Ursula |
| contents | Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_θP_V(E)=m$ or $\dim_θP_V(E)=\dim_θE$ for $γ_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more general functions that include orthogonal projections and fractional Brownian motion. As a particular case, letting $θ=1$, the results are valid for the Box dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical values for Intermediate and Box dimension of projections and other images Angelini, Nicolas Molter, Ursula Classical Analysis and ODEs Probability 28A80, 28A75, 60G22 Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_θP_V(E)=m$ or $\dim_θP_V(E)=\dim_θE$ for $γ_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more general functions that include orthogonal projections and fractional Brownian motion. As a particular case, letting $θ=1$, the results are valid for the Box dimension. |
| title | Critical values for Intermediate and Box dimension of projections and other images |
| topic | Classical Analysis and ODEs Probability 28A80, 28A75, 60G22 |
| url | https://arxiv.org/abs/2501.16598 |