Self-affine sets with positive Lebesgue measure

Dajani, Karma; Jiang, Kan; Kempton, Thomas Michael William

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Date

27/06/2014

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Abstract

Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.

Citation

Dajani , K , Jiang , K & Kempton , T M W 2014 , ' Self-affine sets with positive Lebesgue measure ' , Indagationes Mathematicae , vol. 25 , no. 4 , pp. 774-784 . https://doi.org/10.1016/j.indag.2014.04.009

Publication

Indagationes Mathematicae

Status

Peer reviewed

DOI

https://doi.org/10.1016/j.indag.2014.04.009

ISSN

0019-3577

Type

Journal article

Rights

© 2014, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.indag.2014.04.009

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/7718