Annales Academię Scientiarum Fennicę
Mathematica
Volumen 38, 2013, 473-487

DIMENSION OF SLICES THROUGH A SELF-SIMILAR SET WITH INITIAL CUBIC PATTERN

Zhixiong Wen, Wen Wu and Lifeng Xi

Huazhong University of Science and Technology, School of Mathematics and Statistics
430074, Wuhan, P.R. China; zhi-xiong.wen 'at' mail.hust.edu.cn

Huazhong University of Science and Technology, School of Mathematics and Statistics
430074, Wuhan, P.R. China; hust.wuwen 'at' gmail.com

Zhejiang Wanli University, Institute of Mathematics
315100, Ningbo, P.R. China; xilifengningbo 'at' yahoo.com

Abstract. In this paper, we give a sufficient condition to ensure that the typical Hausdorff dimension of slices through a self-similar set in a fixed direction takes the value in Marstrand's theorem, i.e., the dimension of the self-similar set minus one.

2010 Mathematics Subject Classification: Primary 28A80.

Key words: Self-similar set, slice, Hausdorff dimension, box dimension.

Reference to this article: Z. Wen, W. Wu and L. Xi: Dimension of slices through a self-similar set with initial cubic pattern. Ann. Acad. Sci. Fenn. Math. 38 (2013), 473-487.

Full document as PDF file

doi:10.5186/aasfm.2013.3836

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