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Abstract:

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.

Registro:

Documento: Artículo
Título:The topological reconstruction of forced oscillators
Autor:Solari, H.G.; Natiello, M.A.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab, I 1428 Buenos Aires, Argentina
Center for Mathematical Sciences, Lund University, Box 118, 221 00 LUND, Sweden
Palabras clave:3-dimensional; Forced oscillators; Marangoni convection; Periodic orbits; Phase spaces; Phase variables; Chaotic systems; Phase space methods; Oscillators (electronic)
Año:2009
Volumen:42
Número:4
Página de inicio:2023
Página de fin:2034
DOI: http://dx.doi.org/10.1016/j.chaos.2009.03.167
Título revista:Chaos, Solitons and Fractals
Título revista abreviado:Chaos Solitons Fractals
ISSN:09600779
CODEN:CSFOE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09600779_v42_n4_p2023_Solari

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Citas:

---------- APA ----------
Solari, H.G. & Natiello, M.A. (2009) . The topological reconstruction of forced oscillators. Chaos, Solitons and Fractals, 42(4), 2023-2034.
http://dx.doi.org/10.1016/j.chaos.2009.03.167
---------- CHICAGO ----------
Solari, H.G., Natiello, M.A. "The topological reconstruction of forced oscillators" . Chaos, Solitons and Fractals 42, no. 4 (2009) : 2023-2034.
http://dx.doi.org/10.1016/j.chaos.2009.03.167
---------- MLA ----------
Solari, H.G., Natiello, M.A. "The topological reconstruction of forced oscillators" . Chaos, Solitons and Fractals, vol. 42, no. 4, 2009, pp. 2023-2034.
http://dx.doi.org/10.1016/j.chaos.2009.03.167
---------- VANCOUVER ----------
Solari, H.G., Natiello, M.A. The topological reconstruction of forced oscillators. Chaos Solitons Fractals. 2009;42(4):2023-2034.
http://dx.doi.org/10.1016/j.chaos.2009.03.167