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• # Artykuł - szczegóły

## Studia Mathematica

2015 | 229 | 3 | 223-232

## Multidimensional self-affine sets: non-empty interior and the set of uniqueness

EN

### Abstrakty

EN
Let M be a d × d real contracting matrix. We consider the self-affine iterated function system {Mv-u, Mv+u}, where u is a cyclic vector. Our main result is as follows: if $|det M| ≥ 2^{-1/d}$, then the attractor $A_{M}$ has non-empty interior.
We also consider the set $𝒰_{M}$ of points in $A_{M}$ which have a unique address. We show that unless M belongs to a very special (non-generic) class, the Hausdorff dimension of $𝒰_{M}$ is positive. For this special class the full description of $𝒰_{M}$ is given as well.
This paper continues our work begun in two previous papers.

223-232

wydano
2015

### Twórcy

autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
autor
• School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom