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The box and Hausdorff dimension of self-affine sets

Published online by Cambridge University Press:  19 September 2008

Tim Bedford  and
Mariusz Urbański
Tim Bedford
Affiliation:
Department of Mathematics and Informatics, Delft University of Technology, PO Box 356, 2600 AJ Delft, The Netherlands
Mariusz Urbański
Affiliation:
Intytut Matematyki, Uniwersytet M. Kopernika, ul. Chopina 12/18, 87–100 Toruń, Poland
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Abstract

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Under a natural assumption the Hausdorff dimension of a measure μ canonically associated with a given self-affine set is computed. A simplified proof of Bowen's formula for the box dimension of self-affine sets proved earlier is given. A condition for the box dimension and Hausdorff dimension to be equal is proven, and a collection of examples in which this condition can be checked is discussed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 4 , December 1990 , pp. 627 - 644
Copyright
Copyright © Cambridge University Press 1990

References

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