Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points

Autores
Díaz Ruelas, Alvaro; Fuentes, Miguel Angel; Robledo, Jorge Alberto
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self-affinity in the chaotic region imprints scaling features to the crossover distributions along the sequence of band-splitting points. The trajectories that give rise to these distributions are governed first by the sequential formation of phase-space gaps when, initially uniformly distributed, sets of trajectories evolve towards the chaotic band attractors. Subsequently, the summation of positions of trajectories already within the chaotic bands closes those gaps. The possible shapes of the resultant distributions depend crucially on the disposal of sets of early positions in the sums and the stoppage of the number of terms retained in them.
Fil: Díaz Ruelas, Alvaro. Universidad Nacional Autónoma de México; México
Fil: Fuentes, Miguel Angel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Sistemas Complejos de Valparaíso; Chile. Santa Fe Institute; Estados Unidos. Instituto de Investigaciones Filosóficas - Sadaf; Argentina
Fil: Robledo, Jorge Alberto. Universidad Nacional Autónoma de México; México
Materia
Low-dimensional chaos
Numerical simulations of chaotic systems
Renormalization group methods
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:11336/98988
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Scaling of distributions of sums of positions for chaotic dynamics at band-splitting pointsDíaz Ruelas, AlvaroFuentes, Miguel AngelRobledo, Jorge AlbertoLow-dimensional chaosNumerical simulations of chaotic systemsRenormalization group methodshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self-affinity in the chaotic region imprints scaling features to the crossover distributions along the sequence of band-splitting points. The trajectories that give rise to these distributions are governed first by the sequential formation of phase-space gaps when, initially uniformly distributed, sets of trajectories evolve towards the chaotic band attractors. Subsequently, the summation of positions of trajectories already within the chaotic bands closes those gaps. The possible shapes of the resultant distributions depend crucially on the disposal of sets of early positions in the sums and the stoppage of the number of terms retained in them.Fil: Díaz Ruelas, Alvaro. Universidad Nacional Autónoma de México; MéxicoFil: Fuentes, Miguel Angel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Sistemas Complejos de Valparaíso; Chile. Santa Fe Institute; Estados Unidos. Instituto de Investigaciones Filosóficas - Sadaf; ArgentinaFil: Robledo, Jorge Alberto. Universidad Nacional Autónoma de México; MéxicoEurophysics Letters2014-10info: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/11336/98988Díaz Ruelas, Alvaro; Fuentes, Miguel Angel; Robledo, Jorge Alberto; Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points; Europhysics Letters; Europhysics Letters; 108; 2; 10-2014; 1-50295-5075CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1209/0295-5075/108/20008info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1209/0295-5075/108/20008info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1409.7449info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:53:52Zoai:ri.conicet.gov.ar:11336/98988instacron: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:34982025-10-15 14:53:52.344CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
title Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
spellingShingle Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
Díaz Ruelas, Alvaro
Low-dimensional chaos
Numerical simulations of chaotic systems
Renormalization group methods
title_short Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
title_full Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
title_fullStr Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
title_full_unstemmed Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
title_sort Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points
dc.creator.none.fl_str_mv Díaz Ruelas, Alvaro
Fuentes, Miguel Angel
Robledo, Jorge Alberto
author Díaz Ruelas, Alvaro
author_facet Díaz Ruelas, Alvaro
Fuentes, Miguel Angel
Robledo, Jorge Alberto
author_role author
author2 Fuentes, Miguel Angel
Robledo, Jorge Alberto
author2_role author
author
dc.subject.none.fl_str_mv Low-dimensional chaos
Numerical simulations of chaotic systems
Renormalization group methods
topic Low-dimensional chaos
Numerical simulations of chaotic systems
Renormalization group methods
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self-affinity in the chaotic region imprints scaling features to the crossover distributions along the sequence of band-splitting points. The trajectories that give rise to these distributions are governed first by the sequential formation of phase-space gaps when, initially uniformly distributed, sets of trajectories evolve towards the chaotic band attractors. Subsequently, the summation of positions of trajectories already within the chaotic bands closes those gaps. The possible shapes of the resultant distributions depend crucially on the disposal of sets of early positions in the sums and the stoppage of the number of terms retained in them.
Fil: Díaz Ruelas, Alvaro. Universidad Nacional Autónoma de México; México
Fil: Fuentes, Miguel Angel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto de Sistemas Complejos de Valparaíso; Chile. Santa Fe Institute; Estados Unidos. Instituto de Investigaciones Filosóficas - Sadaf; Argentina
Fil: Robledo, Jorge Alberto. Universidad Nacional Autónoma de México; México
description The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of chaos and a Gaussian trivial fixed-point distribution for all chaotic attractors. Here we describe in detail the crossover distributions that can be generated at chaotic band-splitting points that mediate between the aforementioned fixed-point distributions. Self-affinity in the chaotic region imprints scaling features to the crossover distributions along the sequence of band-splitting points. The trajectories that give rise to these distributions are governed first by the sequential formation of phase-space gaps when, initially uniformly distributed, sets of trajectories evolve towards the chaotic band attractors. Subsequently, the summation of positions of trajectories already within the chaotic bands closes those gaps. The possible shapes of the resultant distributions depend crucially on the disposal of sets of early positions in the sums and the stoppage of the number of terms retained in them.
publishDate 2014
dc.date.none.fl_str_mv 2014-10
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/11336/98988
Díaz Ruelas, Alvaro; Fuentes, Miguel Angel; Robledo, Jorge Alberto; Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points; Europhysics Letters; Europhysics Letters; 108; 2; 10-2014; 1-5
0295-5075
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98988
identifier_str_mv Díaz Ruelas, Alvaro; Fuentes, Miguel Angel; Robledo, Jorge Alberto; Scaling of distributions of sums of positions for chaotic dynamics at band-splitting points; Europhysics Letters; Europhysics Letters; 108; 2; 10-2014; 1-5
0295-5075
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1209/0295-5075/108/20008
info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1209/0295-5075/108/20008
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1409.7449
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 Europhysics Letters
publisher.none.fl_str_mv Europhysics Letters
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 13.22299

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