Properties of some overlapping self-similar and some self-affine measures

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Properties of some overlapping self-similar and some self-affine measures. / Neunhäuserer, Jörg.
In: Acta Mathematica Hungarica, Vol. 92, No. 1-2, 07.2001, p. 143-161.

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@article{7c1bbbfb6c5b494c8486f51d3361b8ca,
title = "Properties of some overlapping self-similar and some self-affine measures",
abstract = "We generalize theorems of Peres and Solomyak about the abso- lute continuity resp. singularity of Bernoulli convolutions ([19], [16], [17]) to a broader class of self-similar measures on the real line. Using the dimension the- ory of ergodic measures (see [11] and [2]) we find a formula for the dimension of certain self-affine measures in terms of the dimension of the above mentioned self- similar measures. Combining these results we show the identity of Hausdorff and box-counting dimension of a special class of self-affine sets.",
keywords = "Mathematics, self-similar, self-affine, Hausdorff dimension, box-counting dimension",
author = "J{\"o}rg Neunh{\"a}userer",
year = "2001",
month = jul,
doi = "10.1023/A:1013716430425",
language = "English",
volume = "92",
pages = "143--161",
journal = "Acta Mathematica Hungarica",
issn = "0236-5294",
publisher = "Springer",
number = "1-2",

}

RIS

TY - JOUR

T1 - Properties of some overlapping self-similar and some self-affine measures

AU - Neunhäuserer, Jörg

PY - 2001/7

Y1 - 2001/7

N2 - We generalize theorems of Peres and Solomyak about the abso- lute continuity resp. singularity of Bernoulli convolutions ([19], [16], [17]) to a broader class of self-similar measures on the real line. Using the dimension the- ory of ergodic measures (see [11] and [2]) we find a formula for the dimension of certain self-affine measures in terms of the dimension of the above mentioned self- similar measures. Combining these results we show the identity of Hausdorff and box-counting dimension of a special class of self-affine sets.

AB - We generalize theorems of Peres and Solomyak about the abso- lute continuity resp. singularity of Bernoulli convolutions ([19], [16], [17]) to a broader class of self-similar measures on the real line. Using the dimension the- ory of ergodic measures (see [11] and [2]) we find a formula for the dimension of certain self-affine measures in terms of the dimension of the above mentioned self- similar measures. Combining these results we show the identity of Hausdorff and box-counting dimension of a special class of self-affine sets.

KW - Mathematics

KW - self-similar

KW - self-affine

KW - Hausdorff dimension

KW - box-counting dimension

U2 - 10.1023/A:1013716430425

DO - 10.1023/A:1013716430425

M3 - Journal articles

VL - 92

SP - 143

EP - 161

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 1-2

ER -

DOI