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Probabilistic approximation of partly filled-in composite Julia sets
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Albaha University, Faculty of Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2017 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, no 3, p. 203-220Article in journal (Refereed) Published
Abstract [en]

We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.

Place, publisher, year, edition, pages
2017. Vol. 119, no 3, p. 203-220
Keywords [en]
composite Julia sets, pluricomplex Green functions, iterated function system, the chaos game, complex dynamics, Monte-Carlo simulation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-339527DOI: 10.4064/ap4100-8-2017ISI: 000417986400002OAI: oai:DiVA.org:uu-339527DiVA, id: diva2:1176368
Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-07-06Bibliographically approved
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Alghamdi, AzzaKlimek, Maciej

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