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On Weierstrass-like functions and random recurrent sets

Published online by Cambridge University Press:  28 June 2011

Tim Bedford
Tim Bedford
Affiliation:
Department of Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands
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Abstract

A construction of Weierstrass-like functions using recurrent sets is described, and the Hausdorff dimensions of the graphs computed. An important part of the proof is the notion of a globally random recurrent set. The Hausdorff dimension of a class of such sets is calculated using techniques of random matrix products.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 325 - 342
Copyright
Copyright © Cambridge Philosophical Society 1989

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