On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings

Autores
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We are interested in the preservation of doubling properties along the Hutchinson orbit generated by successive applications of contraction mappings on a metric measure space. We construct some elementary examples, built on Muckenhoupt weights, showing that even when the initial and the limit points of the orbit are doubling, no iteration of the IFS remains doubling. We also obtain positive results under some quantitative assumptions on the separation of the images through the IFS. We also explore the completeness, in the Hausdorff-Kantorovich metric, of a version of the doubling property which is suitable for the application of Hutchinson type contractions.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
Hutchinson Orbits
Metric Measure Space
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84240
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the Uniform Doubling of Hutchinson Orbits of Contractive MappingsAimar, Hugo AlejandroCarena, MarilinaIaffei, Bibiana RaquelHutchinson OrbitsMetric Measure Spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We are interested in the preservation of doubling properties along the Hutchinson orbit generated by successive applications of contraction mappings on a metric measure space. We construct some elementary examples, built on Muckenhoupt weights, showing that even when the initial and the limit points of the orbit are doubling, no iteration of the IFS remains doubling. We also obtain positive results under some quantitative assumptions on the separation of the images through the IFS. We also explore the completeness, in the Hausdorff-Kantorovich metric, of a version of the doubling property which is suitable for the application of Hutchinson type contractions.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaInstituto de Matemática Aplicada del Litoral2008-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84240Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings ; Instituto de Matemática Aplicada del Litoral; Cuadernos de Matemática y Mecánica; 2008; 12-2008; 1-132314-0992CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://cimec.org.ar/ojs/index.php/cmm/article/view/1387info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:09:37Zoai:ri.conicet.gov.ar:11336/84240instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:09:37.674CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
title On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
spellingShingle On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
Aimar, Hugo Alejandro
Hutchinson Orbits
Metric Measure Space
title_short On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
title_full On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
title_fullStr On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
title_full_unstemmed On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
title_sort On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Carena, Marilina
Iaffei, Bibiana Raquel
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Carena, Marilina
Iaffei, Bibiana Raquel
author_role author
author2 Carena, Marilina
Iaffei, Bibiana Raquel
author2_role author
author
dc.subject.none.fl_str_mv Hutchinson Orbits
Metric Measure Space
topic Hutchinson Orbits
Metric Measure Space
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We are interested in the preservation of doubling properties along the Hutchinson orbit generated by successive applications of contraction mappings on a metric measure space. We construct some elementary examples, built on Muckenhoupt weights, showing that even when the initial and the limit points of the orbit are doubling, no iteration of the IFS remains doubling. We also obtain positive results under some quantitative assumptions on the separation of the images through the IFS. We also explore the completeness, in the Hausdorff-Kantorovich metric, of a version of the doubling property which is suitable for the application of Hutchinson type contractions.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description We are interested in the preservation of doubling properties along the Hutchinson orbit generated by successive applications of contraction mappings on a metric measure space. We construct some elementary examples, built on Muckenhoupt weights, showing that even when the initial and the limit points of the orbit are doubling, no iteration of the IFS remains doubling. We also obtain positive results under some quantitative assumptions on the separation of the images through the IFS. We also explore the completeness, in the Hausdorff-Kantorovich metric, of a version of the doubling property which is suitable for the application of Hutchinson type contractions.
publishDate 2008
dc.date.none.fl_str_mv 2008-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/84240
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings ; Instituto de Matemática Aplicada del Litoral; Cuadernos de Matemática y Mecánica; 2008; 12-2008; 1-13
2314-0992
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84240
identifier_str_mv Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings ; Instituto de Matemática Aplicada del Litoral; Cuadernos de Matemática y Mecánica; 2008; 12-2008; 1-13
2314-0992
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://cimec.org.ar/ojs/index.php/cmm/article/view/1387
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Instituto de Matemática Aplicada del Litoral
publisher.none.fl_str_mv Instituto de Matemática Aplicada del Litoral
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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