Self-similar sets in doubling spaces

Balogh, Zoltán M.; Rohner, Heiner

Illinois J. Math., Tome 51 (2007) no. 3, p. 1275-1297 / Harvested from Project Euclid

Résumé

We extend the well-known Moran-Hutchinson Theorem, which says that under the open set condition the Hausdorff dimension of self-similar sets coincides with the similarity dimension, to the more general setting of doubling metric spaces and prove its reverse implication. We also provide examples of iterated function systems in doubling metric spaces where our results apply.

Publié le : 2007-10-15
Classification: 28A78, 28A80

@article{1258138544,
     author = {Balogh, Zolt\'an M. and Rohner, Heiner},
     title = {Self-similar sets in doubling spaces},
     journal = {Illinois J. Math.},
     volume = {51},
     number = {3},
     year = {2007},
     pages = { 1275-1297},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138544}
}

Balogh, Zoltán M.; Rohner, Heiner. Self-similar sets in doubling spaces. Illinois J. Math., Tome 51 (2007) no. 3, pp.  1275-1297. http://gdmltest.u-ga.fr/item/1258138544/