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Variational formula related to the self‐affine Sierpinski carpets
Author(s) -
Gui Yongxin,
Li Wenxia,
Xiao Dongmei
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400210
Subject(s) - mathematics , sierpinski triangle , affine transformation , uncountable set , hausdorff space , infimum and supremum , hausdorff dimension , combinatorics , discrete mathematics , fractal , pure mathematics , mathematical analysis , countable set
We consider those subsets of the self‐affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.