The topological reconstruction of forced oscillators

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 di...

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Autores principales: Solari, H.G., Natiello, M.A.
Formato: JOUR
Materias:
3-dimensional
Forced oscillators
Marangoni convection
Periodic orbits
Phase spaces
Phase variables
Chaotic systems
Phase space methods
Oscillators (electronic)
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09600779_v42_n4_p2023_Solari
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_09600779_v42_n4_p2023_Solari
record_format dspace
spelling todo:paper_09600779_v42_n4_p2023_Solari2023-10-03T15:53:35Z The topological reconstruction of forced oscillators Solari, H.G. Natiello, M.A. 3-dimensional Forced oscillators Marangoni convection Periodic orbits Phase spaces Phase variables Chaotic systems Phase space methods Oscillators (electronic) 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, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09600779_v42_n4_p2023_Solari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 3-dimensional
Forced oscillators
Marangoni convection
Periodic orbits
Phase spaces
Phase variables
Chaotic systems
Phase space methods
Oscillators (electronic)
spellingShingle 3-dimensional
Forced oscillators
Marangoni convection
Periodic orbits
Phase spaces
Phase variables
Chaotic systems
Phase space methods
Oscillators (electronic)
Solari, H.G.
Natiello, M.A.
The topological reconstruction of forced oscillators
topic_facet 3-dimensional
Forced oscillators
Marangoni convection
Periodic orbits
Phase spaces
Phase variables
Chaotic systems
Phase space methods
Oscillators (electronic)
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.
format JOUR
author Solari, H.G.
Natiello, M.A.
author_facet Solari, H.G.
Natiello, M.A.
author_sort Solari, H.G.
title The topological reconstruction of 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 topological reconstruction of forced oscillators
url http://hdl.handle.net/20.500.12110/paper_09600779_v42_n4_p2023_Solari
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AT natielloma thetopologicalreconstructionofforcedoscillators
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AT natielloma topologicalreconstructionofforcedoscillators
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