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On a class of fractals: the constructive structure

✍ Scribed by S.P. Zhou; G.L. He; T.F. Xie

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
104 KB
Volume
19
Category
Article
ISSN
0960-0779

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✦ Synopsis

In the present paper, we consider the following generalization of Besicovitch functions. Let fk n g satisfy Hadamard condition, write

We are interested in the intrinsic relationship among the coefficients fa n g, the modulus of continuity of f and the upper Box dimension of graph of f . Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware.

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For the contracting similarities S x s xr3, S x s xq r3, and S x s 1 2 3 Ž . w x xq2 r3, where g 0, 1 , let F denote the invariant set with respect to S , S , 1 2 and S . In this paper, we study the Hausdorff measure, Hausdorff dimension, and 3 w x Ž . the structure of F . Let s bra g ‫ޑ‬ l 0, 1 , a