Renormalization group structure for sums of variables generated by incipiently chaotic maps

Autores
Fuentes, Miguel Angel; Robledo, Alberto
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.
Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Pontificia Universidad Católica de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Robledo, Alberto. Universidad Nacional Autónoma de México; México
Materia
NONLINEAR DYNAMICS
RENORMALIZATION GROUP
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:11336/124980
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Renormalization group structure for sums of variables generated by incipiently chaotic mapsFuentes, Miguel AngelRobledo, AlbertoNONLINEAR DYNAMICSRENORMALIZATION GROUPhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Pontificia Universidad Católica de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Robledo, Alberto. Universidad Nacional Autónoma de México; MéxicoIOP Publishing2010-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/124980Fuentes, Miguel Angel; Robledo, Alberto; Renormalization group structure for sums of variables generated by incipiently chaotic maps; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2010; 1; 1-2010; 1-131742-5468CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1742-5468/2010/01/P01001/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2010/01/P01001info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/0912.2930info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:02:20Zoai:ri.conicet.gov.ar:11336/124980instacron: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 11:02:20.715CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Renormalization group structure for sums of variables generated by incipiently chaotic maps
title Renormalization group structure for sums of variables generated by incipiently chaotic maps
spellingShingle Renormalization group structure for sums of variables generated by incipiently chaotic maps
Fuentes, Miguel Angel
NONLINEAR DYNAMICS
RENORMALIZATION GROUP
title_short Renormalization group structure for sums of variables generated by incipiently chaotic maps
title_full Renormalization group structure for sums of variables generated by incipiently chaotic maps
title_fullStr Renormalization group structure for sums of variables generated by incipiently chaotic maps
title_full_unstemmed Renormalization group structure for sums of variables generated by incipiently chaotic maps
title_sort Renormalization group structure for sums of variables generated by incipiently chaotic maps
dc.creator.none.fl_str_mv Fuentes, Miguel Angel
Robledo, Alberto
author Fuentes, Miguel Angel
author_facet Fuentes, Miguel Angel
Robledo, Alberto
author_role author
author2 Robledo, Alberto
author2_role author
dc.subject.none.fl_str_mv NONLINEAR DYNAMICS
RENORMALIZATION GROUP
topic NONLINEAR DYNAMICS
RENORMALIZATION GROUP
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.
Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Pontificia Universidad Católica de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Robledo, Alberto. Universidad Nacional Autónoma de México; México
description We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables.
publishDate 2010
dc.date.none.fl_str_mv 2010-01
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/11336/124980
Fuentes, Miguel Angel; Robledo, Alberto; Renormalization group structure for sums of variables generated by incipiently chaotic maps; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2010; 1; 1-2010; 1-13
1742-5468
CONICET Digital
CONICET
url http://hdl.handle.net/11336/124980
identifier_str_mv Fuentes, Miguel Angel; Robledo, Alberto; Renormalization group structure for sums of variables generated by incipiently chaotic maps; IOP Publishing; Journal of Statistical Mechanics: Theory and Experiment; 2010; 1; 1-2010; 1-13
1742-5468
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://iopscience.iop.org/article/10.1088/1742-5468/2010/01/P01001/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2010/01/P01001
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/0912.2930
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
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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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