Statistics – Computation
Scientific paper
Apr 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrva..37.3118v&link_type=abstract
Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 37, April 15, 1988, p. 3118-3125.
Statistics
Computation
29
Chaos, Dimensions, Fractals, Near Fields, Strange Attractors, Computational Fluid Dynamics, Degrees Of Freedom, Equations Of Motion, Scaling Laws, Spectral Methods, Spectrum Analysis
Scientific paper
Procedures for estimating the dimensions of strange attractors and other fractal sets from the distribution of near-neighbor distances is developed analytically, applying the thermodynamic formalism of Benzi et al. (1984) and Halsey et al. (1986) to establish a firm basis for the algorithms proposed by Pettis et al. (1979), Somorjai (1986), Termonia and Alexandrowicz (1983), and Guckenheimer and Buzyna (1983). Numerical results for time series generated by iterations of the baker transformation (Farmer et al., 1983) are presented graphically, and corrections due to the finite size of the data set are indicated. The present method is shown to be efficient in high-dimensional phase spaces and to permit practical computation of the spectrum of Renyi dimensions from an experimental signal (as in the case of fully developed fluid turbulence).
Schram P. P.
van de Water Willem
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