Abstract
We prove that if μ is a self-affine measure in the plane whose defining IFS acts totally irreducibly on RP1 and satisfies an exponential separation condition, then its dimension is equal to its Lyapunov dimension.We also treat a class of reducible systems. This extends our previous work on the subject with Bárány to the overlapping case.
| Original language | English |
|---|---|
| Pages (from-to) | 2361-2441 |
| Number of pages | 81 |
| Journal | Journal of the European Mathematical Society |
| Volume | 24 |
| Issue number | 7 |
| DOIs | |
| State | Published - 2022 |
Keywords
- Hausdorff dimension
- Lyapunov dimension
- self-affine measure
- self-affine set
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics
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