Sums of variables at the onset of chaos

Autores
Fuentes, Miguel Angel; Robledo, Alberto
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.
Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad del Desarrollo; Chile
Fil: Robledo, Alberto. Universidad Nacional Autónoma de México; México
Materia
Onset of Chaos
Limit Distributions
Maps
Deterministic
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:11336/27397
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Sums of variables at the onset of chaosFuentes, Miguel AngelRobledo, AlbertoOnset of ChaosLimit DistributionsMapsDeterministichttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad del Desarrollo; ChileFil: Robledo, Alberto. Universidad Nacional Autónoma de México; MéxicoSpringer2014-02-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/27397Fuentes, Miguel Angel; Robledo, Alberto; Sums of variables at the onset of chaos; Springer; European Physical Journal B - Condensed Matter; 87; 32; 5-2-2014; 1-71434-6028CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1140/epjb/e2014-40882-1info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1140%2Fepjb%2Fe2014-40882-1info:eu-repo/semantics/altIdentifier/url/https://www.epj.org/images/stories/news/2014/epj_b_02-02-14.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:52:23Zoai:ri.conicet.gov.ar:11336/27397instacron: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 11:52:24.036CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sums of variables at the onset of chaos
title Sums of variables at the onset of chaos
spellingShingle Sums of variables at the onset of chaos
Fuentes, Miguel Angel
Onset of Chaos
Limit Distributions
Maps
Deterministic
title_short Sums of variables at the onset of chaos
title_full Sums of variables at the onset of chaos
title_fullStr Sums of variables at the onset of chaos
title_full_unstemmed Sums of variables at the onset of chaos
title_sort Sums of variables at the onset of chaos
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 Onset of Chaos
Limit Distributions
Maps
Deterministic
topic Onset of Chaos
Limit Distributions
Maps
Deterministic
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 explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.
Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad del Desarrollo; Chile
Fil: Robledo, Alberto. Universidad Nacional Autónoma de México; México
description We explain how specific dynamical properties give rise to the limit distribution of sums of deterministic variables at the transition to chaos via the period-doubling route. We study the sums of successive positions generated by an ensemble of initial conditions uniformly distributed in the entire phase space of a unimodal map as represented by the logistic map. We find that these sums acquire their salient, multiscale, features from the repellor preimage structure that dominates the dynamics toward the attractors along the period-doubling cascade. And we explain how these properties transmit from the sums to their distribution. Specifically, we show how the stationary distribution of sums of positions at the Feigebaum point is built up from those associated with the supercycle attractors forming a hierarchical structure with multifractal and discrete scale invariance properties.
publishDate 2014
dc.date.none.fl_str_mv 2014-02-05
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/11336/27397
Fuentes, Miguel Angel; Robledo, Alberto; Sums of variables at the onset of chaos; Springer; European Physical Journal B - Condensed Matter; 87; 32; 5-2-2014; 1-7
1434-6028
CONICET Digital
CONICET
url http://hdl.handle.net/11336/27397
identifier_str_mv Fuentes, Miguel Angel; Robledo, Alberto; Sums of variables at the onset of chaos; Springer; European Physical Journal B - Condensed Matter; 87; 32; 5-2-2014; 1-7
1434-6028
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1140/epjb/e2014-40882-1
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1140%2Fepjb%2Fe2014-40882-1
info:eu-repo/semantics/altIdentifier/url/https://www.epj.org/images/stories/news/2014/epj_b_02-02-14.pdf
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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