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Random affine code tree fractals and Falconer-Sloan condition
Univ Oulu, Dept Math Sci, POB 3000, Oulu 90014, Finland..
Univ Oulu, Dept Math Sci, POB 3000, Oulu 90014, Finland..
Univ Oulu, Dept Math Sci, POB 3000, Oulu 90014, Finland.;South China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 36, no 5, p. 1516-1533Article in journal (Refereed) Published
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Abstract [en]

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).

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2016. Vol. 36, no 5, p. 1516-1533
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Mathematics
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URN: urn:nbn:se:uu:diva-301014DOI: 10.1017/etds.2014.122ISI: 000379946400009OAI: oai:DiVA.org:uu-301014DiVA: diva2:953415
Available from: 2016-08-17 Created: 2016-08-17 Last updated: 2017-11-28Bibliographically approved

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Stenflo, Örjan

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