Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings
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...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/5698021 |
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| author | Azza Alghamdi Maciej Klimek Marta Kosek |
| author_facet | Azza Alghamdi Maciej Klimek Marta Kosek |
| author_sort | Azza Alghamdi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fa4e88e4181446a3918e642cc72b52ae |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-fa4e88e4181446a3918e642cc72b52ae2025-02-03T07:24:18ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/56980215698021Attractors of Compactly Generated Semigroups of Regular Polynomial MappingsAzza Alghamdi0Maciej Klimek1Marta Kosek2Department of Mathematics, Faculty of Science, Albaha University, Al Baha, Saudi ArabiaDepartment of Mathematics, Uppsala University, P.O. Box 480, 751-06 Uppsala, SwedenInstitute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, PolandWe 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.http://dx.doi.org/10.1155/2018/5698021 |
| spellingShingle | Azza Alghamdi Maciej Klimek Marta Kosek Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings Complexity |
| title | Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings |
| title_full | Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings |
| title_fullStr | Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings |
| title_full_unstemmed | Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings |
| title_short | Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings |
| title_sort | attractors of compactly generated semigroups of regular polynomial mappings |
| url | http://dx.doi.org/10.1155/2018/5698021 |
| work_keys_str_mv | AT azzaalghamdi attractorsofcompactlygeneratedsemigroupsofregularpolynomialmappings AT maciejklimek attractorsofcompactlygeneratedsemigroupsofregularpolynomialmappings AT martakosek attractorsofcompactlygeneratedsemigroupsofregularpolynomialmappings |