Random affine code tree fractals and Falconer-Sloan condition
2016 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 36, no 5, 1516-1533 p.Article in journal (Refereed) PublishedText
We calculate the almost sure dimension for a general class of random affine code tree fractals in R-d. The result is based on a probabilistic version of the Falconer-Sloan condition C(s) introduced in Falconer and Sloan [Continuity of subadditive pressure for self-affine sets. Real Anal. Exchange 34 (2009), 413-427]. We verify that, in general, systems having a small number of maps do not satisfy condition C(s). However, there exists a natural number n such that for typical systems the family of all iterates up to level n satisfies condition C(s).
Place, publisher, year, edition, pages
2016. Vol. 36, no 5, 1516-1533 p.
IdentifiersURN: urn:nbn:se:uu:diva-301014DOI: 10.1017/etds.2014.122ISI: 000379946400009OAI: oai:DiVA.org:uu-301014DiVA: diva2:953415