TY - JOUR
T1 - Hausdorff and packing dimensions of subsets of Moran fractals with prescribed mixed group frequency of their codings
AU - Li, Wenxia
AU - Olsen, Lars
AU - Wen, Zhiying
PY - 2009/3
Y1 - 2009/3
N2 - We compute the Hausdorff dimension and the packing dimension of subsets of Moran fractals with prescribed mixed group frequencies. For example, if E denotes the set of real numbers x in [0, 1] for which the group of digits {1, 2, 3, 4} in the decimal expansion of x occurs with relative frequency t 1 ∈ [0, 1] and the group of digits {0, 1, 2, 8, 9} in the decimal expansion of x occurs with relative frequency t2 ∈ [0, 1], then our results shows that equation is present where dim H denotes the Hausdorff dimension and dim P denotes the packing dimension. Observe that the two groups of digits with prescribed frequencies, namely {1, 2, 3, 4} and {0, 1, 2, 8, 9}, are mixed, i.e. they are not disjoint. Previous work [LD, O1, V] has investigated the non-mixed case. In this paper we investigate the more difficult problem of finding the Hausdorff dimension and packing dimension of subsets of Moran fractals with prescribed mixed group frequencies.
AB - We compute the Hausdorff dimension and the packing dimension of subsets of Moran fractals with prescribed mixed group frequencies. For example, if E denotes the set of real numbers x in [0, 1] for which the group of digits {1, 2, 3, 4} in the decimal expansion of x occurs with relative frequency t 1 ∈ [0, 1] and the group of digits {0, 1, 2, 8, 9} in the decimal expansion of x occurs with relative frequency t2 ∈ [0, 1], then our results shows that equation is present where dim H denotes the Hausdorff dimension and dim P denotes the packing dimension. Observe that the two groups of digits with prescribed frequencies, namely {1, 2, 3, 4} and {0, 1, 2, 8, 9}, are mixed, i.e. they are not disjoint. Previous work [LD, O1, V] has investigated the non-mixed case. In this paper we investigate the more difficult problem of finding the Hausdorff dimension and packing dimension of subsets of Moran fractals with prescribed mixed group frequencies.
KW - Group frequencies ofdigits
KW - Hausdor?dimension
KW - Mixed group frequencies ofdigits
KW - Packing dimension
UR - https://www.scopus.com/pages/publications/62949160379
U2 - 10.1007/s00010-008-2947-5
DO - 10.1007/s00010-008-2947-5
M3 - 文章
AN - SCOPUS:62949160379
SN - 0001-9054
VL - 77
SP - 171
EP - 185
JO - Aequationes Mathematicae
JF - Aequationes Mathematicae
IS - 1-2
ER -