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- Title
Estimating singularity dimension.
- Authors
POLLICOTT, M.; VYTNOVA, P.
- Abstract
In this paper we address an interesting question on the computation of the dimension of self-affine sets in Euclidean space. A well-known result of Falconer showed that under mild assumptions the Hausdorff dimension of typical self-affine sets is equal to its Singularity dimension. Heuter and Lalley subsequently presented a smaller open family of non-trivial examples for which there is an equality of these two dimensions. In this article we analyse the size of this family and present an efficient algorithm for estimating the dimension.
- Subjects
MATHEMATICAL singularities; ESTIMATION theory; DIMENSIONS; FRACTAL dimensions; SET theory
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2015, Vol 158, Issue 2, p223
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S030500411400053X