Self-affine sets with positive Lebesgue measure

Karma Dajani; Kan Jiang; Thomas Michael William Kempton

doi:10.1016/j.indag.2014.04.009

Self-affine sets with positive Lebesgue measure

Karma Dajani, Kan Jiang, Thomas Michael William Kempton

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	774-784
Journal	Indagationes Mathematicae
Volume	25
Issue number	4
Early online date	9 May 2014
DOIs	https://doi.org/10.1016/j.indag.2014.04.009
Publication status	Published - 27 Jun 2014

Keywords

Overlapping self-affine sets
Iterated function systems
Beta expansions

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10.1016/j.indag.2014.04.009

Self Affine Sets with Positive Lebesgue Measure
© 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
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Cite this

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title = "Self-affine sets with positive Lebesgue measure",

abstract = "Using techniques introduced by C. Gunturk, we prove that the attractors of afamily 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 {\textquoteleft}simultaneousβ-expansion{\textquoteright} of different numbers in different bases.",

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AU - Jiang, Kan

AU - Kempton, Thomas Michael William

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AB - Using techniques introduced by C. Gunturk, we prove that the attractors of afamily 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 ‘simultaneousβ-expansion’ of different numbers in different bases.

KW - Overlapping self-affine sets

KW - Iterated function systems

KW - Beta expansions

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Self-affine sets with positive Lebesgue measure

Abstract

Keywords

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