The dimension of projections of planar diagonal self-affine measures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916597769175040 |
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| author | Pyörälä, Aleksi |
| author_facet | Pyörälä, Aleksi |
| contents | We show that if $μ$ is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts, $$ \dim_{\rm H} μ\circ π^{-1}= \min\lbrace 1,\dim_{\rm H}μ\rbrace $$ for any non-principal orthogonal projection $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The dimension of projections of planar diagonal self-affine measures Pyörälä, Aleksi Dynamical Systems 28A80 (Primary), 37A10 (Secondary) We show that if $μ$ is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts, $$ \dim_{\rm H} μ\circ π^{-1}= \min\lbrace 1,\dim_{\rm H}μ\rbrace $$ for any non-principal orthogonal projection $π$. |
| title | The dimension of projections of planar diagonal self-affine measures |
| topic | Dynamical Systems 28A80 (Primary), 37A10 (Secondary) |
| url | https://arxiv.org/abs/2410.03401 |