Equidistribution from fractal measures

Autores
Hochman, Michael; Shmerkin, Pablo Sebastian
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that (Formula presented.) equidistributes modulo 1. This condition is robust under C1 coordinate changes, and it applies also when n is a Pisot number rather than an integer. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host’s theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.
Fil: Hochman, Michael. The Hebrew University of Jerusalem; Israel
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. University of Surrey. Faculty of Engineering and Physical Sciences. Department of Mathematics; Reino Unido. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Equidistribution
Fractals
Resonance
Normal Numbers
11k16
11a63
28a80
28d05
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:11336/38161
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/38161
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network_name_str CONICET Digital (CONICET)
spelling Equidistribution from fractal measuresHochman, MichaelShmerkin, Pablo SebastianEquidistributionFractalsResonanceNormal Numbers11k1611a6328a8028d05https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that (Formula presented.) equidistributes modulo 1. This condition is robust under C1 coordinate changes, and it applies also when n is a Pisot number rather than an integer. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host’s theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.Fil: Hochman, Michael. The Hebrew University of Jerusalem; IsraelFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. University of Surrey. Faculty of Engineering and Physical Sciences. Department of Mathematics; Reino Unido. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38161Hochman, Michael; Shmerkin, Pablo Sebastian; Equidistribution from fractal measures; Springer; Inventiones Mathematicae; 202; 1; 10-2015; 427-4790020-9910CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00222-014-0573-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-014-0573-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:20:54Zoai:ri.conicet.gov.ar:11336/38161instacron: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:34982025-10-22 12:20:54.546CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Equidistribution from fractal measures
title Equidistribution from fractal measures
spellingShingle Equidistribution from fractal measures
Hochman, Michael
Equidistribution
Fractals
Resonance
Normal Numbers
11k16
11a63
28a80
28d05
title_short Equidistribution from fractal measures
title_full Equidistribution from fractal measures
title_fullStr Equidistribution from fractal measures
title_full_unstemmed Equidistribution from fractal measures
title_sort Equidistribution from fractal measures
dc.creator.none.fl_str_mv Hochman, Michael
Shmerkin, Pablo Sebastian
author Hochman, Michael
author_facet Hochman, Michael
Shmerkin, Pablo Sebastian
author_role author
author2 Shmerkin, Pablo Sebastian
author2_role author
dc.subject.none.fl_str_mv Equidistribution
Fractals
Resonance
Normal Numbers
11k16
11a63
28a80
28d05
topic Equidistribution
Fractals
Resonance
Normal Numbers
11k16
11a63
28a80
28d05
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 give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that (Formula presented.) equidistributes modulo 1. This condition is robust under C1 coordinate changes, and it applies also when n is a Pisot number rather than an integer. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host’s theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.
Fil: Hochman, Michael. The Hebrew University of Jerusalem; Israel
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. University of Surrey. Faculty of Engineering and Physical Sciences. Department of Mathematics; Reino Unido. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that (Formula presented.) equidistributes modulo 1. This condition is robust under C1 coordinate changes, and it applies also when n is a Pisot number rather than an integer. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host’s theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/38161
Hochman, Michael; Shmerkin, Pablo Sebastian; Equidistribution from fractal measures; Springer; Inventiones Mathematicae; 202; 1; 10-2015; 427-479
0020-9910
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38161
identifier_str_mv Hochman, Michael; Shmerkin, Pablo Sebastian; Equidistribution from fractal measures; Springer; Inventiones Mathematicae; 202; 1; 10-2015; 427-479
0020-9910
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://link.springer.com/article/10.1007/s00222-014-0573-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00222-014-0573-5
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
publisher.none.fl_str_mv Springer
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 12.982451

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