On the dimensions of a family of overlapping self-affine carpets

Autores
Fraser, Jonathan; Shmerkin, Pablo Sebastian
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman´s recent work on the dimensions of self-similar sets and measures.
Fil: Fraser, Jonathan. University of Manchester; Reino Unido
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Materia
SELF-AFFINE CARPET
HAUSDORFF DIMENSION
PACKING DIMENSION
BOX DIMENSION
OVERLAPS
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:11336/53255
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the dimensions of a family of overlapping self-affine carpetsFraser, JonathanShmerkin, Pablo SebastianSELF-AFFINE CARPETHAUSDORFF DIMENSIONPACKING DIMENSIONBOX DIMENSIONOVERLAPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman´s recent work on the dimensions of self-similar sets and measures.Fil: Fraser, Jonathan. University of Manchester; Reino UnidoFil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaCambridge University Press2016-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/53255Fraser, Jonathan; Shmerkin, Pablo Sebastian; On the dimensions of a family of overlapping self-affine carpets; Cambridge University Press; Ergodic Theory And Dynamical Systems; 36; 8; 12-2016; 2463-24810143-3857CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/div-classtitleon-the-dimensions-of-a-family-of-overlapping-self-affine-carpetsdiv/1D8911F0FA764104328BC41A235603D5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:44:46Zoai:ri.conicet.gov.ar:11336/53255instacron: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:34982025-09-29 10:44:47.064CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the dimensions of a family of overlapping self-affine carpets
title On the dimensions of a family of overlapping self-affine carpets
spellingShingle On the dimensions of a family of overlapping self-affine carpets
Fraser, Jonathan
SELF-AFFINE CARPET
HAUSDORFF DIMENSION
PACKING DIMENSION
BOX DIMENSION
OVERLAPS
title_short On the dimensions of a family of overlapping self-affine carpets
title_full On the dimensions of a family of overlapping self-affine carpets
title_fullStr On the dimensions of a family of overlapping self-affine carpets
title_full_unstemmed On the dimensions of a family of overlapping self-affine carpets
title_sort On the dimensions of a family of overlapping self-affine carpets
dc.creator.none.fl_str_mv Fraser, Jonathan
Shmerkin, Pablo Sebastian
author Fraser, Jonathan
author_facet Fraser, Jonathan
Shmerkin, Pablo Sebastian
author_role author
author2 Shmerkin, Pablo Sebastian
author2_role author
dc.subject.none.fl_str_mv SELF-AFFINE CARPET
HAUSDORFF DIMENSION
PACKING DIMENSION
BOX DIMENSION
OVERLAPS
topic SELF-AFFINE CARPET
HAUSDORFF DIMENSION
PACKING DIMENSION
BOX DIMENSION
OVERLAPS
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 consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman´s recent work on the dimensions of self-similar sets and measures.
Fil: Fraser, Jonathan. University of Manchester; Reino Unido
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
description We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman´s recent work on the dimensions of self-similar sets and measures.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
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/11336/53255
Fraser, Jonathan; Shmerkin, Pablo Sebastian; On the dimensions of a family of overlapping self-affine carpets; Cambridge University Press; Ergodic Theory And Dynamical Systems; 36; 8; 12-2016; 2463-2481
0143-3857
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53255
identifier_str_mv Fraser, Jonathan; Shmerkin, Pablo Sebastian; On the dimensions of a family of overlapping self-affine carpets; Cambridge University Press; Ergodic Theory And Dynamical Systems; 36; 8; 12-2016; 2463-2481
0143-3857
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://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/div-classtitleon-the-dimensions-of-a-family-of-overlapping-self-affine-carpetsdiv/1D8911F0FA764104328BC41A235603D5
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/zip
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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 13.070432

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