Self-Affine Sets with Positive Lebesgue Measure

Karma Dajani; Kan Jiang; Tom Kempton

doi:10.1016/j.indag.2014.04.009

Self-Affine Sets with Positive Lebesgue Measure

Karma Dajani, Kan Jiang, Tom Kempton

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

Abstract

Using techniques introduced by C. G ̈unt ̈urk, 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
Number of pages	11
Journal	Indagationes Mathematicae
Volume	25
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2014.04.009
Publication status	Published - 2014

Keywords

Overlapping self-affine sets
Iterated function systems
β-expansions

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10.1016/j.indag.2014.04.009

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title = "Self-Affine Sets with Positive Lebesgue Measure",

abstract = "Using techniques introduced by C. G{\" }unt{\" }urk, 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 {\textquoteleft}simultaneous β-expansion{\textquoteright} of different numbers in different bases",

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AU - Dajani, Karma

AU - Jiang, Kan

AU - Kempton, Tom

PY - 2014

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AB - Using techniques introduced by C. G ̈unt ̈urk, 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

KW - Overlapping self-affine sets

KW - Iterated function systems

KW - β-expansions

U2 - 10.1016/j.indag.2014.04.009

DO - 10.1016/j.indag.2014.04.009

M3 - Article

SN - 0019-3577

VL - 25

SP - 774

EP - 784

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -

Self-Affine Sets with Positive Lebesgue Measure

Abstract

Keywords

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