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2003 Dimensions of the Boundaries of Self-Similar Sets
Ka-Sing Lau, Sze-Man Ngai
Experiment. Math. 12(1): 13-26 (2003).

Abstract

We introduce a finite boundary type condition on iterated function systems of contractive similitudes on $\R^d$ Under this condition, we compute the Hausdorff dimension of the boundary of the attractor in terms of the spectral radius of some finite offspring matrix. We describe how to construct such a matrix. We also show that, in this case, the box dimension equals the Hausdorff dimension. In particular, this allows us to compute the Hausdorff dimension of the boundary of a class of self-similar sets defined by expansion matrices with noninteger entries.

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Ka-Sing Lau. Sze-Man Ngai. "Dimensions of the Boundaries of Self-Similar Sets." Experiment. Math. 12 (1) 13 - 26, 2003.

Information

Published: 2003
First available in Project Euclid: 29 September 2003

zbMATH: 1054.28006
MathSciNet: MR2002671

Subjects:
Primary: 28A78
Secondary: 28A80

Keywords: box dimension , finite boundary type condition , finite type condition , Hausdorff dimension , self-affine tile , self-similar set , self-similar tile

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 1 • 2003
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