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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/37425
Ver los metadatos del registro completo
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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 |
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CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
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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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1844614440919498752 |
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13.070432 |