Hausdorff dimension of asymptotic self-similar sets
Daruhan Wu
University of Tsukuba, Japan and Inner Mongolia University of Finance and Economics, Huhhan, ChinaTakao Yamaguchi
Kyoto University, Japan
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Abstract
In this paper, we introduce the notion of asymptotic self-similar sets on general doubling metric spaces by extending the notion of self-similar sets, and determine their Hausdorff dimensions, which gives an extension of Balogh and Rohner’s result. This is carried out by introducing the notions of almost similarity maps and asymptotic similarity systems. These notions have an advantage of making geometric constructions possible. Actually, as an application, we determined the Hausdorff dimension of general Sierpinski gaskets on complete surfaces constructed by a geometric way in a natural manner.
Cite this article
Daruhan Wu, Takao Yamaguchi, Hausdorff dimension of asymptotic self-similar sets. J. Fractal Geom. 4 (2017), no. 4, pp. 339–368
DOI 10.4171/JFG/54