The topological reconstruction of forced oscillators
- Autores
- Solari, Hernan Gustavo; Natiello, Mario A.
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2 × S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Bénard-Marangoni convection. © 2009 Elsevier Ltd. All rights reserved.
Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Natiello, Mario A.. Lund University; Suecia - Materia
-
Chaos
Topology
Forced Oscillators - 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:11336/60741
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The topological reconstruction of forced oscillatorsSolari, Hernan GustavoNatiello, Mario A.ChaosTopologyForced Oscillatorshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2 × S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Bénard-Marangoni convection. © 2009 Elsevier Ltd. All rights reserved.Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Natiello, Mario A.. Lund University; SueciaPergamon-Elsevier Science Ltd2009-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60741Solari, Hernan Gustavo; Natiello, Mario A.; The topological reconstruction of forced oscillators; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 42; 4; 12-2009; 2023-20340960-0779CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2009.03.167info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:40:08Zoai:ri.conicet.gov.ar:11336/60741instacron: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 09:40:08.571CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The topological reconstruction of forced oscillators |
title |
The topological reconstruction of forced oscillators |
spellingShingle |
The topological reconstruction of forced oscillators Solari, Hernan Gustavo Chaos Topology Forced Oscillators |
title_short |
The topological reconstruction of forced oscillators |
title_full |
The topological reconstruction of forced oscillators |
title_fullStr |
The topological reconstruction of forced oscillators |
title_full_unstemmed |
The topological reconstruction of forced oscillators |
title_sort |
The topological reconstruction of forced oscillators |
dc.creator.none.fl_str_mv |
Solari, Hernan Gustavo Natiello, Mario A. |
author |
Solari, Hernan Gustavo |
author_facet |
Solari, Hernan Gustavo Natiello, Mario A. |
author_role |
author |
author2 |
Natiello, Mario A. |
author2_role |
author |
dc.subject.none.fl_str_mv |
Chaos Topology Forced Oscillators |
topic |
Chaos Topology Forced Oscillators |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2 × S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Bénard-Marangoni convection. © 2009 Elsevier Ltd. All rights reserved. Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Natiello, Mario A.. Lund University; Suecia |
description |
Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2 × S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems. In this work we show that, in general, it is not possible to produce a 3-dimensional imbedding of the solutions of a forced oscillator in terms of differential imbeddings based on sampling the position only. However, it may be possible to uncover a description of the phase variable from the sampled time-series, thus producing a faithful representation of the data. We proceed to formulate new tests in order to check whether proposed imbeddings can be accepted as such. We illustrate the manuscript throughout with an example corresponding to a model of Bénard-Marangoni convection. © 2009 Elsevier Ltd. All rights reserved. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-12 |
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/11336/60741 Solari, Hernan Gustavo; Natiello, Mario A.; The topological reconstruction of forced oscillators; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 42; 4; 12-2009; 2023-2034 0960-0779 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/60741 |
identifier_str_mv |
Solari, Hernan Gustavo; Natiello, Mario A.; The topological reconstruction of forced oscillators; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 42; 4; 12-2009; 2023-2034 0960-0779 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2009.03.167 |
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 |
Pergamon-Elsevier Science Ltd |
publisher.none.fl_str_mv |
Pergamon-Elsevier Science Ltd |
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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1844613269794324480 |
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13.070432 |