Self-affine sets with positive Lebesgue measure
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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.
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 . DOI: 10.1016/j.indag.2014.04.009
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