TY - JOUR
T1 - Measure and dimension for some fractal families
AU - Solomyak, Boris
PY - 1998/11
Y1 - 1998/11
N2 - We study self-similar sets with overlaps, on the line and in the plane. It is shown that there exist self-similar sets that have non-integral Hausdorff dimension equal to the similarity dimension, but with zero Hausdorff measure. In many cases the Hausdorff dimension is computed for a typical parameter value. We also explore conditions for the validity of Falconer's formula for the Hausdorff dimension of self-affine sets, and study the dimension of some fractal graphs.
AB - We study self-similar sets with overlaps, on the line and in the plane. It is shown that there exist self-similar sets that have non-integral Hausdorff dimension equal to the similarity dimension, but with zero Hausdorff measure. In many cases the Hausdorff dimension is computed for a typical parameter value. We also explore conditions for the validity of Falconer's formula for the Hausdorff dimension of self-affine sets, and study the dimension of some fractal graphs.
UR - http://www.scopus.com/inward/record.url?scp=33746803712&partnerID=8YFLogxK
U2 - 10.1017/s0305004198002680
DO - 10.1017/s0305004198002680
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AN - SCOPUS:33746803712
SN - 0305-0041
VL - 124
SP - 531
EP - 546
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 3
ER -