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Exceptional sets for self-affine fractals

Published online by Cambridge University Press:  01 November 2008

KENNETH FALCONER  and
JUN MIAO
KENNETH FALCONER
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS. e-mail: kjf@st-and.ac.uk, jjm38@st-and.ac.uk
JUN MIAO
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS. e-mail: kjf@st-and.ac.uk, jjm38@st-and.ac.uk
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Abstract

Under certain conditions the ‘singular value function’ formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 669 - 684
Copyright
Copyright © Cambridge Philosophical Society 2008

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