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Exceptional sets for self-similar fractals in Carnot groups
Published online by Cambridge University Press: 24 March 2010
Abstract
We consider self-similar iterated function systems in the sub-Riemannian setting of Carnot groups. We estimate the Hausdorff dimension of the exceptional set of translation parameters for which the Hausdorff dimension in terms of the Carnot–Carathéodory metric is strictly less than the similarity dimension. This extends a recent result of Falconer and Miao from Euclidean space to Carnot groups.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 147 - 172
- Copyright
- Copyright © Cambridge Philosophical Society 2010
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