Non-invertible planar self-affine sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912133111873536 |
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| author | Käenmäki, Antti Nissinen, Petteri |
| author_facet | Käenmäki, Antti Nissinen, Petteri |
| contents | We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamical formalism where, for dominated and irreducible matrices, we completely characterize the behavior of the pressures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07351 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-invertible planar self-affine sets Käenmäki, Antti Nissinen, Petteri Dynamical Systems Primary 28A80, Secondary 37C45, 37D35 We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamical formalism where, for dominated and irreducible matrices, we completely characterize the behavior of the pressures. |
| title | Non-invertible planar self-affine sets |
| topic | Dynamical Systems Primary 28A80, Secondary 37C45, 37D35 |
| url | https://arxiv.org/abs/2205.07351 |