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HAUSDORFF DIMENSION OF SELF-SIMILAR SETS WITH OVERLAPS

Published online by Cambridge University Press:  05 July 2001

SZE-MAN NGAI  and
YANG WANG
SZE-MAN NGAI
Affiliation:
School of Mathematics, Georgia Institute of Technology , Atlanta, Georgia 30332, USA; [email protected], [email protected] Current address: Department of Mathematics and Computer Science, Georgia Southern University, Statesboro, GA 30460, USA; [email protected]
YANG WANG
Affiliation:
School of Mathematics, Georgia Institute of Technology , Atlanta, Georgia 30332, USA; [email protected], [email protected]
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Abstract

The notion of ‘finite type’ iterated function systems of contractive similitudes is introduced, and a scheme for computing the exact Hausdorff dimension of their attractors in the absence of the open set condition is described. This method extends a previous one by Lalley, and applies not only to the classes of self-similar sets studied by Edgar, Lalley, Rao and Wen, and others, but also to some new classes that are not covered by the previous ones.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 655 - 672
Copyright
The London Mathematical Society 2001

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