Enlarged scaling ranges for the KS-entropy and the information dimension.

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data. (c) 1996 American Institute of Physics.

[1]  Peter Grassberger,et al.  Generalizations of the Hausdorff dimension of fractal measures , 1985 .

[2]  Schreiber,et al.  Nonlinear noise reduction: A case study on experimental data. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  A. Politi,et al.  HOMOCLINIC TANGENCIES, GENERATING PARTITIONS AND CURVATURE OF INVARIANT MANIFOLDS , 1991 .

[4]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[5]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[6]  Cohen,et al.  Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems. , 1985, Physical review. A, General physics.

[7]  P. Bösiger,et al.  Solid-State Nuclear Spin-Flip Maser Pumped by Dynamic Nuclear Polarization , 1977 .

[8]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[9]  P. Grassberger.  Toward a quantitative theory of self-generated complexity , 1986 .

[10]  P. Grassberger.  Generalized dimensions of strange attractors , 1983 .

[11]  Christiansen,et al.  Generating partition for the standard map. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  P. Grassberger,et al.  Generating partitions for the dissipative Hénon map , 1985 .

[13]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[14]  P. Grassberger.  Finite sample corrections to entropy and dimension estimates , 1988 .

[15]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[16]  P. Billingsley,et al.  Ergodic theory and information , 1966 .

[17]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[18]  A. Politi,et al.  Statistical description of chaotic attractors: The dimension function , 1985 .

[19]  Werner Ebeling,et al.  Entropy of symbolic sequences: the role of correlations , 1991 .

[20]  P. Gaspard,et al.  Noise, chaos, and (ε,τ)-entropy per unit time , 1993 .