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Maximum likelihood method for evaluating correlation dimension

  • Robert Cawley
  • A. Lewis Licht
A. Classical Nonlinear Dynamics and Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 278)

Keywords

Chaotic System Correlation Dimension Dynamical System Theory Slope Function Embedding Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    See, for instance, J. Doyne Farmer, Edward Ott and James A. Yorke, Physica 7D, 153 (1983) for discussion of a variety of notions of dimension.ADSGoogle Scholar
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    John Guckenheimer in “Dynamical Systems and Chaos”, L. Garrido, ed., L. N. Physics, No. 179, Springer-Verlag, Berlin, 1983. Guckenheimer attributes the delay-coordinate embedding procedure as apparently due to Ruelle, see also Ref. 12. Formulation of the procedure in the context of dynamical systems theory is given by Takens in Ref. 13. Also, the first physical demonstration of the representation of a system in a higher dimensional space from a single time-series, as well as the intuitive idea of the embedding procedure, was given in Ref. [12].Google Scholar
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    W. E. Caswell and J. A. Yorke, “Invisible Errors in Dimension Calculations: Geometric and Systematic Effects”, in “Dimensions and Entropies in Chaotic Systems”, G. Mayer-Kress, ed., Synergetics Series, Springer-Verlag, Berlin, 1986.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Robert Cawley
    • 1
  • A. Lewis Licht
    • 1
  1. 1.Naval Surface Weapons CenterWhite Oak, Silver Spring

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