Separation properties for iterated function systems of bounded distortion

In this paper we study a general separation property for subsystems G, whose attractor KG is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we chara...

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Detalles Bibliográficos
Autores: Panzone, Pablo Andres, Ferrari, Mariano Andrés
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/15458
Acceso en línea:http://hdl.handle.net/11336/15458
Access Level:acceso abierto
Palabra clave:FRACTALS
HAUSDORFF DIMENSION
OVERLAPPING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Separation properties for iterated function systems of bounded distortionPanzone, Pablo AndresFerrari, Mariano AndrésFRACTALSHAUSDORFF DIMENSIONOVERLAPPINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study a general separation property for subsystems G, whose attractor KG is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we characterize the subsets of KG with positive measure where the separation property may fail. We exhibit two examples of fractal sets, one not satisfying the weak separation property and whose existence was questioned by Zerner, the other having positive Hausdorff measure in its dimension and with the separation property failing on a subset of positive measure.Fil: Panzone, Pablo Andres. Universidad Nacional de la Patagonia; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Ferrari, Mariano Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaWorld Scientific2011-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15458Panzone, Pablo Andres; Ferrari, Mariano Andrés; Separation properties for iterated function systems of bounded distortion; World Scientific; Fractals; 19; 3; 9-2011; 259-2690218-348Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0218348X11005361info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0218348X11005361info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:39:04Zoai:ri.conicet.gov.ar:11336/15458instacron: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:34982024-05-08 13:39:04.541CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Separation properties for iterated function systems of bounded distortion
title Separation properties for iterated function systems of bounded distortion
spellingShingle Separation properties for iterated function systems of bounded distortion
Panzone, Pablo Andres
FRACTALS
HAUSDORFF DIMENSION
OVERLAPPING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Separation properties for iterated function systems of bounded distortion
title_full Separation properties for iterated function systems of bounded distortion
title_fullStr Separation properties for iterated function systems of bounded distortion
title_full_unstemmed Separation properties for iterated function systems of bounded distortion
title_sort Separation properties for iterated function systems of bounded distortion
dc.creator.none.fl_str_mv Panzone, Pablo Andres
Ferrari, Mariano Andrés
author Panzone, Pablo Andres
author_facet Panzone, Pablo Andres
Ferrari, Mariano Andrés
author_role author
author2 Ferrari, Mariano Andrés
author2_role author
dc.subject.none.fl_str_mv FRACTALS
HAUSDORFF DIMENSION
OVERLAPPING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic FRACTALS
HAUSDORFF DIMENSION
OVERLAPPING
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper we study a general separation property for subsystems G, whose attractor KG is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we characterize the subsets of KG with positive measure where the separation property may fail. We exhibit two examples of fractal sets, one not satisfying the weak separation property and whose existence was questioned by Zerner, the other having positive Hausdorff measure in its dimension and with the separation property failing on a subset of positive measure.
publishDate 2011
dc.date.none.fl_str_mv 2011-09
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/11336/15458
Panzone, Pablo Andres; Ferrari, Mariano Andrés; Separation properties for iterated function systems of bounded distortion; World Scientific; Fractals; 19; 3; 9-2011; 259-269
0218-348X
url http://hdl.handle.net/11336/15458
identifier_str_mv Panzone, Pablo Andres; Ferrari, Mariano Andrés; Separation properties for iterated function systems of bounded distortion; World Scientific; Fractals; 19; 3; 9-2011; 259-269
0218-348X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218348X11005361
info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0218348X11005361
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
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,812429

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