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- Alghamdi, Azza, et al.
(author)
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Attractors of compactly generated semigroups of regular polynomial mappings.
- 2018
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In: Complexity. - : Hindawi Limited. - 1076-2787 .- 1099-0526.
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Journal article (peer-reviewed)abstract
- We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.
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| 3. |
- Klimek, Maciej, et al.
(author)
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Generalized iterated function systems, multifunctions and Cantor sets
- 2009
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In: Annales Polonici Mathematici. - Warsaw : IM PAN. - 0066-2216 .- 1730-6272. ; 96:1, s. 25-41
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Journal article (peer-reviewed)abstract
- Using a construction similar to an iterated function system, but withfunctions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.
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| 4. |
- Klimek, Maciej, et al.
(author)
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On the metric space of pluriregular sets
- 2018
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In: Dolomites Research Notes on Approximation. - 2035-6803. ; 11:Special issue, s. 51-61
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Journal article (peer-reviewed)abstract
- The metric space of pluriregular sets was introduced over two decades ago but to this day most of its topological properties remain a mystery. The purpose of this short survey is to present the current state of knowledge concerning this space.
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