Geodesic
Probabilistic approximation of partly filled-in composite Julia sets
Azza Alghamdi1 ; Maciej Klimek2
1 Department of Mathematics Faculty of Science Albaha University Al Baha, Saudi Arabia and Department of Mathematics Uppsala University P.O. Box 480 751 06 Uppsala, Sweden
2 Department of Mathematics Uppsala University P.O. Box 480 751 06 Uppsala, Sweden
Annales Polonici Mathematici, Tome 119 (2017) no. 3, pp. 203-220 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap4100-8-2017
Keywords: study properties metric space pluriregular sets contractions space induced finite families proper polynomial mappings several complex variables particular closed balls space pluriregular sets have compact simple proof applicability so called chaos game composite julia sets part construction those sets leads computationally viable approximation simpler sets based monte carlo simulation

Azza Alghamdi 1 ; Maciej Klimek 2

1 Department of Mathematics Faculty of Science Albaha University Al Baha, Saudi Arabia and Department of Mathematics Uppsala University P.O. Box 480 751 06 Uppsala, Sweden
2 Department of Mathematics Uppsala University P.O. Box 480 751 06 Uppsala, Sweden 
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Azza Alghamdi; Maciej Klimek. Probabilistic approximation of partly filled-in composite Julia sets. Annales Polonici Mathematici, Tome 119 (2017) no. 3, pp. 203-220. doi: 10.4064/ap4100-8-2017

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