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Maximum likelihood method for evaluating correlation dimension

  • A. Classical Nonlinear Dynamics and Chaos
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The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function

Part of the book series: Lecture Notes in Physics ((LNP,volume 278))

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References

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  3. 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.

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  14. 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].

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Y. S. Kim W. W. Zachary

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© 1987 Springer-Verlag

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Cawley, R., Licht, A.L. (1987). Maximum likelihood method for evaluating correlation dimension. In: Kim, Y.S., Zachary, W.W. (eds) The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Lecture Notes in Physics, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17894-5_329

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  • DOI: https://doi.org/10.1007/3-540-17894-5_329

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  • Online ISBN: 978-3-540-47901-7

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