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
© 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