Skip to main content
SpringerLink
Log in

On an Embedding Theorem

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We prove a theorem giving conditions under which a discrete-time dynamical system as (x t ,y t ) = (f;(x t − 1, y t − 1), g(x t − 1, y t − 1)) can be reconstructed from a scalar valued time series (α t ) t , which depends only on x t where α t = α(x t ). This theorem allows us to use the delay-coordinate method in this setting.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Abraham and J. Robbin, Transversal Mapping and Flows, W. D. Benjamin (New York, 1967).

    Google Scholar 

  2. C. D. Cutler, A review of the theory and estimation of fractal dimension, in: Dimension, Estimation and Models. (H. Tong, editor), Wold Scientific (1993), pp. 1–107.

  3. J. P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Review Modern Physics, 57 (1985), 617–656.

    Google Scholar 

  4. M. J. Foster, Calculus on vector bundles, J. London Math. Soc., 11 (1975), 65–73.

    Google Scholar 

  5. M. W. Hirsch, Differential Topology, Springer Verlag, fifth edition (1994).

  6. L. Noakes, The Takens embedding theorem, International Journal of Bifurcation and Chaos, 1 (1991), 867–872.

    Google Scholar 

  7. E. Ott, T. Sauer and J. A. Yorke, editors, Coping with Chaos, John Wiley & Sons (1994).

  8. C. Robinson, Dynamical Systems. Stability, Symbolic Dynamic, and Chaos, CRC Press (London, 1995).

    Google Scholar 

  9. T. Sauer, J. A. Yorke and M. Casdagli, Embedology, Journal of Statistic Physics, 65 (1991), 579–616.

    Google Scholar 

  10. J. Stark, Delay embedding for forced systems: I. Deterministic forcing, Journal Nonlinear Science (1999, to appear).

  11. J. Stark, D. S. Broomhead, M. E. Davies and J. Huke, Takens embedding theorem for forced and stochastic systems, Nonlinear Analysis, Theory, Methods and Applications, 30 (1997), 5303–5314.

    Google Scholar 

  12. F. Takens, Detecting strange attractors in turbulence, Lecture Notes in Mathematics, 898 (1981), 366–381.

  13. H. Whitney, Differentiable manifolds, Annals of Math., 37 (1936), 645–680.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Métodos Cuantitativos Para La Economía Facultad de Economía y Empressa Campus de Espinardo, Universidad de Murcia, Murcia, Spain E-mail

    Victoria Caballero

Authors
  1. Victoria Caballero
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caballero, V. On an Embedding Theorem. Acta Mathematica Hungarica 88, 269–278 (2000). https://doi.org/10.1023/A:1026753605784

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026753605784

Keywords

Search

Navigation