Structure of distributions generated by the scenery flow

Autores
Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution (FD) in the sense of Hochman is generated by a USM, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of FDs is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all FDs as tangent distributions.
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 Distribution
Cp-Process
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:11336/37425

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spelling Structure of distributions generated by the scenery flowKäenmäki, AnttiSahlsten, TuomasShmerkin, Pablo SebastianScenery FlowFractal DistributionCp-Processhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution (FD) in the sense of Hochman is generated by a USM, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of FDs is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all FDs as tangent distributions.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; ArgentinaWiley2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/37425Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Structure of distributions generated by the scenery flow; Wiley; Journal Of The London Mathematical Society-second Series; 91; 2; 1-2015; 464-4940024-6107CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdu076info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/jlms/jdu076/abstractinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:41:05Zoai:ri.conicet.gov.ar:11336/37425instacron: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 10:41:05.406CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Structure of distributions generated by the scenery flow
title Structure of distributions generated by the scenery flow
spellingShingle Structure of distributions generated by the scenery flow
Käenmäki, Antti
Scenery Flow
Fractal Distribution
Cp-Process
title_short Structure of distributions generated by the scenery flow
title_full Structure of distributions generated by the scenery flow
title_fullStr Structure of distributions generated by the scenery flow
title_full_unstemmed Structure of distributions generated by the scenery flow
title_sort Structure of distributions generated by the scenery flow
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 Distribution
Cp-Process
topic Scenery Flow
Fractal Distribution
Cp-Process
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 expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution (FD) in the sense of Hochman is generated by a USM, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of FDs is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all FDs as tangent distributions.
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 expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution (FD) in the sense of Hochman is generated by a USM, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of FDs is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all FDs as tangent distributions.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/37425
Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Structure of distributions generated by the scenery flow; Wiley; Journal Of The London Mathematical Society-second Series; 91; 2; 1-2015; 464-494
0024-6107
CONICET Digital
CONICET
url http://hdl.handle.net/11336/37425
identifier_str_mv Käenmäki, Antti; Sahlsten, Tuomas; Shmerkin, Pablo Sebastian; Structure of distributions generated by the scenery flow; Wiley; Journal Of The London Mathematical Society-second Series; 91; 2; 1-2015; 464-494
0024-6107
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdu076
info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/jlms/jdu076/abstract
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 Wiley
publisher.none.fl_str_mv Wiley
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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