Exceptional sets for self-similar fractals in Carnot groups
2010 ◽
Vol 149
(1)
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pp. 147-172
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Keyword(s):
AbstractWe 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.
2019 ◽
Vol 150
(1)
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pp. 261-275
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2011 ◽
Vol 32
(4)
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pp. 1190-1215
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2018 ◽
Vol 106
(1)
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pp. 56-103
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Keyword(s):
2011 ◽
Vol 139
(08)
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pp. 2767-2767
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