Attractors of compactly generated semigroups of regular polynomial mappings
type: Item
instance of: scholarly article
title: Attractors of compactly generated semigroups of regular polynomial mappings
zbMATH Open document ID: 1408.37075
DOI: 10.1155/2018/5698021
author: M. Klimek
author: Marta Kosek
author: Azza M. Alghamdi
published in: Complexity
publication date: 2019-02-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 32A19
zbMATH DE Number: 7025074
zbMATH Keywords: pluriregular sets
zbMATH Keywords: compact attractors
zbMATH Keywords: iterated function systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5698021
OpenAlex ID: W2889202952
cites work: Probabilistic approximation of partly filled-in composite Julia sets
cites work: The Dynamics of Semigroups of Rational Functions I
cites work: Backward iteration algorithms for Julia sets of Möbius semigroups
cites work: Random complex dynamics and semigroups of holomorphic maps
cites work: Random complex dynamics and devil's coliseums
cites work: Metrics Associated with Extremal Plurisubharmonic Functions
cites work: \(V\)-variable fractals: Fractals with partial self similarity
cites work: On perturbations of pluriregular sets generated by sequences of polynomial maps
cites work: Q4002495
cites work: Function theory in the unit ball of \({\mathbb{C}}^ n\)
cites work: Iteration of analytic multifunctions
cites work: Composite Julia sets generated by infinite polynomial arrays.
cites work: Q4354696
cites work: Generalized iteration
cites work: Random iterations of rational functions
cites work: Q4150804
cites work: Q4496194
cites work: Fractals and hyperspaces
cites work: Q3731958
cites work: Random iteration for infinite nonexpansive iterated function systems
Wikidata QID: Q128947535
description: scientific article; zbMATH DE number 7025074