Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings. (11th November 2018)

• Record Type: Journal Article
• Authors: Alghamdi, Azza; Klimek, Maciej; Kosek, Marta
• Other Names: Volchenkov Dimitri Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-11-11
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/5698021
• Languages: English
• ISSNs: 1076-2787

Abstract

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.