Gradual doubling property of Hutchinson orbits

Autores
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The classical self-similar fractals can be obtained as xed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, have both the doubling property. We prove that the elements of Hutchinson orbits satisfy the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
Fil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
Materia
Metric Space
Doubling Measure
Hausdorff-Kantorovich Metric
Iterated Function System
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:11336/13882
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/13882
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Gradual doubling property of Hutchinson orbitsAimar, Hugo AlejandroCarena, MarilinaIaffei, Bibiana RaquelMetric SpaceDoubling MeasureHausdorff-Kantorovich MetricIterated Function Systemhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The classical self-similar fractals can be obtained as xed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, have both the doubling property. We prove that the elements of Hutchinson orbits satisfy the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; ArgentinaFil: Carena, Marilina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; ArgentinaFil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; ArgentinaSpringer Heidelberg2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/13882Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; Gradual doubling property of Hutchinson orbits; Springer Heidelberg; Czechoslovak Mathematical Journal; 65; 1; 11-2015; 191-2050011-46421572-9141enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10587-015-0168-3info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10587-015-0168-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:23:54Zoai:ri.conicet.gov.ar:11336/13882instacron: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:34982025-10-15 14:23:54.502CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Gradual doubling property of Hutchinson orbits
title Gradual doubling property of Hutchinson orbits
spellingShingle Gradual doubling property of Hutchinson orbits
Aimar, Hugo Alejandro
Metric Space
Doubling Measure
Hausdorff-Kantorovich Metric
Iterated Function System
title_short Gradual doubling property of Hutchinson orbits
title_full Gradual doubling property of Hutchinson orbits
title_fullStr Gradual doubling property of Hutchinson orbits
title_full_unstemmed Gradual doubling property of Hutchinson orbits
title_sort Gradual doubling property of Hutchinson orbits
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 Metric Space
Doubling Measure
Hausdorff-Kantorovich Metric
Iterated Function System
topic Metric Space
Doubling Measure
Hausdorff-Kantorovich Metric
Iterated Function System
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The classical self-similar fractals can be obtained as xed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, have both the doubling property. We prove that the elements of Hutchinson orbits satisfy the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
Fil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnol.conicet - Santa Fe. Instituto de Matematica Aplicada "litoral"; Argentina
description The classical self-similar fractals can be obtained as xed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, have both the doubling property. We prove that the elements of Hutchinson orbits satisfy the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
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/11336/13882
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; Gradual doubling property of Hutchinson orbits; Springer Heidelberg; Czechoslovak Mathematical Journal; 65; 1; 11-2015; 191-205
0011-4642
1572-9141
url http://hdl.handle.net/11336/13882
identifier_str_mv Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; Gradual doubling property of Hutchinson orbits; Springer Heidelberg; Czechoslovak Mathematical Journal; 65; 1; 11-2015; 191-205
0011-4642
1572-9141
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10587-015-0168-3
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10587-015-0168-3
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 Springer Heidelberg
publisher.none.fl_str_mv Springer Heidelberg
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 13.22299

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