Weakly controlled Moran constructions and iterated functions systems in metric spaces
Rajala, T., & Vilppolainen, M. (2011). Weakly controlled Moran constructions and iterated functions systems in metric spaces. Illinois Journal of Mathematics, 55(3), 1015-1051. https://doi.org/10.1215/ijm/1369841795
Published inIllinois Journal of Mathematics
© 2013 University of Illinois
We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well-known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.
PublisherUniversity of Illinois
Moran-konstruktio semikonforminen iteroitu funktiojärjestelmä äärellinen pakkautuminen palloehto avoimen joukon ehto Hausdorffin mitta Hausdorff-ulottuvuus Moran construction semiconformal iterated function system finite clustering property ball condition open set condition Hausdorff measure Hausdorff dimension
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