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P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
F. Takens, “Invariants related to dimension and entropy”, in Atas do 13° Coloqkio Brasiliero de Matematica, Rio de Janeiro, 1983, in “Dynamical Systems and Bifurcations”, B. L. J. Braaksma, H. W. Broer and F. Takens, eds., L. N. Mathematics, No. 1125, Springer-Verlag, Berlin, 1985).
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.
P. Grassberger, Phys. Letters 97A, 227 (1983).
H. G. E. Hentschel and I. Procaccia, Physica 8D, 435 (1983); P. Grassberger and I. Procaccia, Physica 13D, 34 (1984).
H. S. Greenside, A. Wolf, J. Swift and T. Pignataro, Phys. Rev. A25, 3453 (1982).
L. P. Kadanoff, in “Perspectives in Nonlinear Dynamics”, M. Shlesinger, R. Cawley, A. W. Saenz and W. W. Zachary, eds., World Scientific, Singapore, 1986; and I. Procaccia, in “Dimensions and Entropies in Chaotic Systems”, G. Mayer-Kress, ed., Synergetics Series, Springer-Verlag, Berlin, 1986.
J. Holzfuss and G. Mayer-Kress, in “Dimensions and Entropies in Chaotic Systems”, G. Mayer-Kress, ed., Synergetics Series, Springer-Verlag, Berlin, 1986.
F. Takens, in “Dynamical Systems and Bifurcations”, B. L. J. Braaksma and H. W. Boer and F. Takens, eds., L. N. Mathematics, No. 1125, Springer-Verlag, Berlin, 1985.
H. D. Brunk, “An Introduction to Mathematical Statistics”, Ginn and Company, Boston, 1960.
M. Henon, Commum. Math. Phys. 50, 69 (1976).
N. H. Packard, J. P. Crutchfield, J. D. Farmer and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980).
F. Takens, in “Dynamical Systems and Turbulence, Warwick, 1980”, D. A. Rand and L.-S. Young, eds., L. N. Mathematics, No. 898, Springer-Verlag, Berlin, 1981.
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].
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.
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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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