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

• Autorzy: Kevin G. Hare , Nikita Sidorov
• Języki publikacji: 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.

Kategorie tematyczne

• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 229
• Numer: 3
• Strony: 223-232

Daty

wydano

2015

Twórcy

autor

Kevin G. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

autor

Nikita Sidorov

• School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

Identyfikatory

DOI

10.4064/sm8359-1-2016