Dynamics of the scenery flow and geometry of measures

Autores
Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its settheoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.
Fil: Käenmäki, Antti. Universidad de Jyvaskyla; Finlandia
Fil: Sahlsten, Tuomas. The Hebrew University of Jerusalem; Israel
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
SCENERY FLOW
FRACTAL DISTRIBUTIONS
DIMENSION
RECITFIABILITY
POROSITY
CONICAL DENSITIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/38583
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Dynamics of the scenery flow and geometry of measuresKäenmäki, AnttiSahlsten, TuomasShmerkin, Pablo SebastianSCENERY FLOWFRACTAL DISTRIBUTIONSDIMENSIONRECITFIABILITYPOROSITYCONICAL DENSITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its settheoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.Fil: Käenmäki, Antti. Universidad de Jyvaskyla; FinlandiaFil: Sahlsten, Tuomas. The Hebrew University of Jerusalem; IsraelFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaLondon Mathematical Society2015-03info: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/11336/38583Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Dynamics of the scenery flow and geometry of measures; London Mathematical Society; Proceedings of the London Mathematical Society; 110; 5; 3-2015; 1248-12800024-6115CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdv003/abstractinfo:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdv003info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1401.0231info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:53:23Zoai:ri.conicet.gov.ar:11336/38583instacron: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 09:53:23.375CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Dynamics of the scenery flow and geometry of measures
title Dynamics of the scenery flow and geometry of measures
spellingShingle Dynamics of the scenery flow and geometry of measures
Käenmäki, Antti
SCENERY FLOW
FRACTAL DISTRIBUTIONS
DIMENSION
RECITFIABILITY
POROSITY
CONICAL DENSITIES
title_short Dynamics of the scenery flow and geometry of measures
title_full Dynamics of the scenery flow and geometry of measures
title_fullStr Dynamics of the scenery flow and geometry of measures
title_full_unstemmed Dynamics of the scenery flow and geometry of measures
title_sort Dynamics of the scenery flow and geometry of measures
dc.creator.none.fl_str_mv Käenmäki, Antti
Sahlsten, Tuomas
Shmerkin, Pablo Sebastian
author Käenmäki, Antti
author_facet Käenmäki, Antti
Sahlsten, Tuomas
Shmerkin, Pablo Sebastian
author_role author
author2 Sahlsten, Tuomas
Shmerkin, Pablo Sebastian
author2_role author
author
dc.subject.none.fl_str_mv SCENERY FLOW
FRACTAL DISTRIBUTIONS
DIMENSION
RECITFIABILITY
POROSITY
CONICAL DENSITIES
topic SCENERY FLOW
FRACTAL DISTRIBUTIONS
DIMENSION
RECITFIABILITY
POROSITY
CONICAL DENSITIES
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 employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its settheoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.
Fil: Käenmäki, Antti. Universidad de Jyvaskyla; Finlandia
Fil: Sahlsten, Tuomas. The Hebrew University of Jerusalem; Israel
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its settheoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.
publishDate 2015
dc.date.none.fl_str_mv 2015-03
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/11336/38583
Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Dynamics of the scenery flow and geometry of measures; London Mathematical Society; Proceedings of the London Mathematical Society; 110; 5; 3-2015; 1248-1280
0024-6115
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38583
identifier_str_mv Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Dynamics of the scenery flow and geometry of measures; London Mathematical Society; Proceedings of the London Mathematical Society; 110; 5; 3-2015; 1248-1280
0024-6115
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdv003/abstract
info:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdv003
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1401.0231
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv London Mathematical Society
publisher.none.fl_str_mv London 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 13.070432

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