We consider self-similar iterated function systems in the sub-Rieman- nian setting of Carnot groups. We estimate the Hausdorff dimension of the exceptional set of translation parameters for which the Hausdorff dimension in terms ofthe Carnot-Carath ́odory metric is strictly less than the similarity dimension. This generalizes a recent result of Falconer and Miao from the Euclidean space to Carnot groups.
Exceptional sets for self-similar fractals in Carnot groups.
MONTI, ROBERTO;
2010
Abstract
We consider self-similar iterated function systems in the sub-Rieman- nian setting of Carnot groups. We estimate the Hausdorff dimension of the exceptional set of translation parameters for which the Hausdorff dimension in terms ofthe Carnot-Carath ́odory metric is strictly less than the similarity dimension. This generalizes a recent result of Falconer and Miao from the Euclidean space to Carnot groups.File in questo prodotto:
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