Properties of quasi-Assouad dimension

Autores
Garcia, Ignacio Andres; Hare, Kathryn
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the x-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimension
Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina
Fil: Hare, Kathryn. University of Waterloo; Canadá
Materia
ASSOUAD DIMENSION
ORTHOGONAL PROJECTIONS
WEAK TANGENTS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/182284
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Properties of quasi-Assouad dimensionGarcia, Ignacio AndresHare, KathrynASSOUAD DIMENSIONORTHOGONAL PROJECTIONSWEAK TANGENTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the x-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimensionFil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; ArgentinaFil: Hare, Kathryn. University of Waterloo; CanadáFinnish Mathematical Society2021-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/182284Garcia, Ignacio Andres; Hare, Kathryn; Properties of quasi-Assouad dimension; Finnish Mathematical Society; Annales Fennici Mathematici; 46; 1; 6-2021; 279-2932737-06902737-114XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://afm.journal.fi/article/view/109582info:eu-repo/semantics/altIdentifier/doi/10.5186/aasfm.2021.4618info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:19:43Zoai:ri.conicet.gov.ar:11336/182284instacron: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:34982025-09-10 13:19:44.154CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Properties of quasi-Assouad dimension
title Properties of quasi-Assouad dimension
spellingShingle Properties of quasi-Assouad dimension
Garcia, Ignacio Andres
ASSOUAD DIMENSION
ORTHOGONAL PROJECTIONS
WEAK TANGENTS
title_short Properties of quasi-Assouad dimension
title_full Properties of quasi-Assouad dimension
title_fullStr Properties of quasi-Assouad dimension
title_full_unstemmed Properties of quasi-Assouad dimension
title_sort Properties of quasi-Assouad dimension
dc.creator.none.fl_str_mv Garcia, Ignacio Andres
Hare, Kathryn
author Garcia, Ignacio Andres
author_facet Garcia, Ignacio Andres
Hare, Kathryn
author_role author
author2 Hare, Kathryn
author2_role author
dc.subject.none.fl_str_mv ASSOUAD DIMENSION
ORTHOGONAL PROJECTIONS
WEAK TANGENTS
topic ASSOUAD DIMENSION
ORTHOGONAL PROJECTIONS
WEAK TANGENTS
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 connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the x-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimension
Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina
Fil: Hare, Kathryn. University of Waterloo; Canadá
description The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the x-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimension
publishDate 2021
dc.date.none.fl_str_mv 2021-06
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/11336/182284
Garcia, Ignacio Andres; Hare, Kathryn; Properties of quasi-Assouad dimension; Finnish Mathematical Society; Annales Fennici Mathematici; 46; 1; 6-2021; 279-293
2737-0690
2737-114X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/182284
identifier_str_mv Garcia, Ignacio Andres; Hare, Kathryn; Properties of quasi-Assouad dimension; Finnish Mathematical Society; Annales Fennici Mathematici; 46; 1; 6-2021; 279-293
2737-0690
2737-114X
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://afm.journal.fi/article/view/109582
info:eu-repo/semantics/altIdentifier/doi/10.5186/aasfm.2021.4618
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Finnish Mathematical Society
publisher.none.fl_str_mv Finnish Mathematical Society
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 12.493442

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