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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Solari, Hernán Gustavo, Natiello, Mario Alberto
Publicado:	2009
Materias:	3-dimensional Forced oscillators Marangoni convection Periodic orbits Phase spaces Phase variables Chaotic systems Phase space methods Oscillators (electronic)
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v42_n4_p2023_Solari 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	paper:paper_09600779_v42_n4_p2023_Solari
record_format	dspace
spelling	paper:paper_09600779_v42_n4_p2023_Solari2023-06-08T15:57:29Z The topological reconstruction of forced oscillators Solari, Hernán Gustavo Natiello, Mario Alberto 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v42_n4_p2023_Solari 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, Hernán Gustavo Natiello, Mario Alberto 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.
author	Solari, Hernán Gustavo Natiello, Mario Alberto
author_facet	Solari, Hernán Gustavo Natiello, Mario Alberto
author_sort	Solari, Hernán Gustavo
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
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v42_n4_p2023_Solari http://hdl.handle.net/20.500.12110/paper_09600779_v42_n4_p2023_Solari
work_keys_str_mv	AT solarihernangustavo thetopologicalreconstructionofforcedoscillators AT natiellomarioalberto thetopologicalreconstructionofforcedoscillators AT solarihernangustavo topologicalreconstructionofforcedoscillators AT natiellomarioalberto topologicalreconstructionofforcedoscillators
_version_	1768541713807179776

The topological reconstruction of forced oscillators

Ejemplares similares