Exceptional projections of self-affine sets: an introduction
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913725888331776 |
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| author | Morris, Ian D. |
| author_facet | Morris, Ian D. |
| contents | We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image. We give a self-contained treatment of this bound and illustrate it through explicit examples, in the process exhibiting some smooth submanifolds of the Grassmannian which can be contained in the exceptional set in Marstrand's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04894 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exceptional projections of self-affine sets: an introduction Morris, Ian D. Dynamical Systems Classical Analysis and ODEs Metric Geometry 28A80 We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image. We give a self-contained treatment of this bound and illustrate it through explicit examples, in the process exhibiting some smooth submanifolds of the Grassmannian which can be contained in the exceptional set in Marstrand's theorem. |
| title | Exceptional projections of self-affine sets: an introduction |
| topic | Dynamical Systems Classical Analysis and ODEs Metric Geometry 28A80 |
| url | https://arxiv.org/abs/2308.04894 |