Resumen de Hausdorff and packing dimensions of subsets of Moran fractals with prescribed mixed group frequency of their codings

Wenxia Li, Lars Olsen, Zhi-Ying Wen

• 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 and the group of digits {0, 1, 2, 8, 9} in the decimal expansion of x occurs with relative frequency , then our results shows that , where dimH denotes the Hausdorff dimension and dimP 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.