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:
| File | Dimensione | Formato | |
|---|---|---|---|
|
InCarnotGroup16.pdf
Accesso riservato
Tipologia:
Published (Publisher's Version of Record)
Licenza:
Accesso privato - non pubblico
Dimensione
309.61 kB
Formato
Adobe PDF
|
309.61 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
