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Dimensions associated with recurrent self-similar sets

Published online by Cambridge University Press:  24 October 2008

Anca Deliu ,
J. S. Geronimo ,
R. Shonkwiler  and
D. Hardin
Anca Deliu
Affiliation:
Georgia Institute of Technology, School of Mathematics, Atlanta, Georgia 30332, U.S.A.
J. S. Geronimo
Affiliation:
Georgia Institute of Technology, School of Mathematics, Atlanta, Georgia 30332, U.S.A.
R. Shonkwiler
Affiliation:
Georgia Institute of Technology, School of Mathematics, Atlanta, Georgia 30332, U.S.A.
D. Hardin
Affiliation:
Vanderbilt University, Department of Mathematics, Nashville, Tennessee 37235, U.S.A.
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Abstract

The Hausdorff and box dimensions for measures associated with recurrent self-similar sets generated by similitudes is explicitly given. The box dimension of the attractor associated with a class of two-dimensional affine maps is also computed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 327 - 336
Copyright
Copyright © Cambridge Philosophical Society 1991

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