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

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Hare K., Sidorov N.

Studia Mathematica

2015

tom 229

nr 3

223-232

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.

Ograniczanie wyników

1 Studia Mathematica

1 Hare K.

1 Sidorov N.

1 2015

Wyniki wyszukiwania

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