next up previous contents
Up: The identification of strange Previous: Effects of correlations between   Contents


Abramowitz and Stegun, 1970
Abramowitz, M. and Stegun, I. (1970).
Handbook of mathematical functions.
Dover Publications, Inc., New York.

Albano et al., 1987
Albano, A., Mees, A., de Guzman, G., and Rapp, P. (1987).
Data requirements for reliable estimation of correlation dimensions.
In Degn, H., Holden, A., and Olsen, L., editors, Chaos in biological systems, page 207. Plenum Press, New York.

Albano et al., 1988
Albano, A., Münch, J., Schwartz, C., Mees, A., and Rapp, P. (1988).
Singular values decomposition and the grassberger-procaccia algorithm.
Phys. Rev. A, 38(6):3017.

Badii and Politi, 1985
Badii, R. and Politi, A. (1985).
Statistical description of chaotic attractors.
J. Stat. Phys., 40(5,6):725.

Barhorst, 1976
Barhorst, T. (1976).
Marquardt-achtige methoden voor de kleinste kwadratenschatting van parameters in niet-lineaire modellen (marquardt-like methods for the least squares estimation of parameters in nonlinear models).
Master's thesis, T.H. Twente, Enschede, The Netherlands.

Beauchamp and Yuen, 1979
Beauchamp, K. and Yuen, C. (1979).
Digital methods for signal analysis.
George Allen & Unwin, London.

Berkenbosch, 1987
Berkenbosch, A. (1987).
Chemical control of breathing.
PhD thesis, University of Leiden, Leiden, The Netherlands.

Broggi, 1988
Broggi, G. (1988).
Evaluation of dimensions and entropies of chaotic systems.
J. Opt. Soc. Am. B, 5(5):1020.

Broomhead and King, 1986
Broomhead, D. and King, G. (1986).
Extracting qualitative dynamics from experimental data.
Physica, 20D:217.

Cremers and Hübler, 1987
Cremers, J. and Hübler, A. (1987).
Construction of differential equations from experimental data.
Z. Naturforsch., 42a:797.

Eckmann and Ruelle, 1985
Eckmann, J.-P. and Ruelle, D. (1985).
Ergodic theory of chaos and strange attractors.
Rev. Mod. Phys., 57(3):617.

Ellner, 1988
Ellner, S. (1988).
Estimating attractor dimensions from limited data: a new method, with error estimates.
Phys. Lett. A, 133(3):128.

Fraser and Swinney, 1986
Fraser, A. and Swinney, H. (1986).
Independent coordinates for strange attractors from mutual information.
Phys. Rev. A, 33(2):1134.

Fukunaga and Hostetler, 1973
Fukunaga, K. and Hostetler, L. (1973).
Optimalization of k-nearest-neighbor density estimates.
IEEE Trans. Inf. Theory, 19:320.

Goldberger et al., 1990
Goldberger, A., Rigney, D., and West, B. (February 1990).
Chaos and fractals in human physiology.
Scientific American, page 34.

Göttsche and Huber,
Göttsche, J. and Huber, A. (?).
Maximum likelihood estimation of local scaling indices.
(Inst. für Theoretische Physik, Kiel), preprint.

Grassberger, 1985
Grassberger, P. (1985).
Generalizations of the Haussdorff dimension of fractal measures.
Phys. Lett., 107A(3):101.

Grassberger, 1986
Grassberger, P. (1986).
Estimating the fractal dimensions and entropies of strange attractors.
In Holden, A., editor, Chaos, page 291. Manchester University Press, Manchester.

Grassberger et al., 1988
Grassberger, P., Badii, R., and Politi, A. (1988).
Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors.
J. Stat. Phys., 51(1,2):135.

Grassberger and Procaccia, 1983a
Grassberger, P. and Procaccia, I. (1983a).
Estimation of the kolmogorov entropy from a chaotic signal.
Phys. Rev. A, 28(4):2591.

Grassberger and Procaccia, 1983b
Grassberger, P. and Procaccia, I. (1983b).
Measuring the strangeness of strange attractors.
Physica, 9D:189.

Grassberger and Procaccia, 1984
Grassberger, P. and Procaccia, I. (1984).
Dimensions and entropies of strange attractors from a fluctuating dynamics approach.
Physica, 13D:34.

Halsey et al., 1986
Halsey, T., Jensen, M., Kadanoff, L., Procaccia, I., and Shraiman, B. (1986).
Fractal measures and their singularities: the characterization of strange sets.
Phys. Rev. A, 33(2):1141.

Hénon, 1976
Hénon, M. (1976).
A two-dimensional mapping with a strange attractor.
Commun. Math. Phys., 50(1):69.

Hogg and Craig, 1978
Hogg, R. and Craig, A. (1978).
Introduction to mathematical statistics.
Macmillan Publishing Co., Inc., New York, 4th edition.

Holden and Muhamad, 1986
Holden, A. and Muhamad, M. (1986).
A graphical zoo of strange and peculiar attractors.
In Holden, A., editor, Chaos, page 15. Manchester University Press, Manchester.

Holzfuss and Mayer-Kress, 1986
Holzfuss, J. and Mayer-Kress, G. (1986).
An approach to error-estimation in the application of dimension algorithms.
In Mayer-Kress, G., editor, Dimensions and entropies in chaotic systems, page 114. Springer, Heidelberg.

Kendall and Stuart, 1979
Kendall, M. and Stuart, A. (1979).
The advanced theory of statistics, volume 2.
Griffin, London, 4th edition.

Kolmogorov, 1959
Kolmogorov, A. (1959).
Entropy per unit time as a metric invariant of automorphisms.
Dokl. Akad. Nauk. SSSR, 124:754.

Kotz and Johnson, 1985
Kotz, S. and Johnson, N. (1985).
Encyclopedia of statistical sciences, volume 5.
Wiley, New York.

Lehmann, 1983
Lehmann, E. (1983).
Theory of point estimation.
Wiley, New York.

Liebert and Schuster, 1989
Liebert, W. and Schuster, H. (1989).
Proper choice of the time delay for the analysis of chaotic time series.

Mayer-Kress, 1987
Mayer-Kress, G. (1987).
Application of dimension algorithms to experimental chaos.
In Bai-lin, H., editor, Directions in chaos, Vol. 1, page 122. World Scientific Publishing Co. Pte. Ltd., Singapore.

Numerical Algorithms Group, 1983
Numerical Algorithms Group (1983).
NAG Fortran Library, Oxford.

Olofsen, 1987
Olofsen, E. (1987).
Dimensionality estimators using near-neighbour information, Internal report, University of Twente, Enschede, The Netherlands.

Ott et al., 1984
Ott, E., Withers, W., and Yorke, J. (1984).
Is the dimension of chaotic attractors invariant under coordinate changes?
J. Stat. Phys., 36(5,6):687.

Packard et al., 1980
Packard, N., Crutchfield, J., Farmer, J., and Shaw, R. (1980).
Geometry from a time series.
Phys. Rev. Lett., 45:712.

Parker and Chua, 1987
Parker, T. and Chua, L. (1987).
Chaos: A tutorial for engineers.
In Proceedings of the IEEE, Vol. 75, page 982. IEEE.

Pawelzik and Schuster, 1987
Pawelzik, K. and Schuster, H. (1987).
Generalized dimensions and entropies from a measured time series.
Phys. Rev. A, 35(1):481.

Pettis et al., 1979
Pettis, K., Bailey, T., Jain, A., and Dubes, R. (1979).
An intrinsic dimensionality estimator from near-neighbor information.
IEEE Trans. Pattern Anal., Mach. Intell., PAMI-1:25.

Procaccia, 1985
Procaccia, I. (1985).
The static and dynamic invariants that characterize chaos and the relations between them in theory and experiments.
Physica Scripta, T9:40.

Renyi, 1970
Renyi, A. (1970).
Probability theory.
North-Holland, Amsterdam.

Rössler, 1976
Rössler, O. (1976).
An equation for continuous chaos.
Phys. Lett., 57A(5):397.

Ruelle, 1990
Ruelle, D. (1990).
Deterministic chaos: the science and the fiction.
Proc. R. Soc. Lond. A, 427:241.

Schuster, 1988
Schuster, H. (1988).
Deterministic chaos, an introduction.
Physik-Verlag, Weinheim, $2^{\mbox{{\small nd}}}$ edition.

Singleton, 1969
Singleton, R. (1969).
Acm algorithm 347.
Comm. of the ACM, 12:1865.
Implementation in MBIV/MI library.

Smith, 1988
Smith, L. (1988).
Intrinsic limits on dimension calculations.
Phys. Lett. A, 133(6):283.

Somorjai, 1986
Somorjai, R. (1986).
Methods for estimating the intrinsic dimensionality of high-dimensional point sets.
In Mayer-Kress, G., editor, Dimensions and entropies in chaotic systems, page 137. Springer, Heidelberg.

Takens, 1981
Takens, F. (1981).
Detecting strange attractors in turbulence.
In Lecture notes in mathematics, Vol.898. Dynamical systems and turbulence, page 366. Springer, Berlin.

Takens, 1983
Takens, F. (1983).
Invariants related to dimension and entropy.
In Atas do $13^{\circ}$. Colóqkio Brasiliero do Matemática, Rio de Janeiro.

Takens, 1985
Takens, F. (1985).
On the numerical determination of the dimension of an attractor.
In Lecture notes in mathematics, Vol.1125. Dynamical systems and bifurcations, page 99. Springer, Berlin.

Takens, 1987
Takens, F. (1987).
Influence of entropy and embedding dimension on algorithms to estimate the dimension of an attractor, private communication.

Termonia and Alexandrowicz, 1983
Termonia, Y. and Alexandrowicz, Z. (1983).
Fractal dimension of strange attractors from radius versus size of arbitrary clusters.
Phys. Rev. Lett., 51(14):1265.

Theiler, 1986
Theiler, J. (1986).
Spurious dimension from correlation algorithms applied to limited time-series data.
Phys. Rev. A, 34(3):2427-2432.

Theiler, 1988
Theiler, J. (1988).
Lacunarity in a best estimator of fractal dimension.
Phys. Lett. A, 133(4,5):195.

Theiler, 1990
Theiler, J. (1990).
Estimating fractal dimension.
J. Opt. Soc. Am. A, 7(6):1055.

van de Water, 1987
van de Water, W. (1987).
private communication (and software).

van de Water and Schram, 1988
van de Water, W. and Schram, P. (1988).
Generalized dimensions from near-neighbour information.
Phys. Rev. A, 37(8):3118.

van Erp, 1988
van Erp, M. (1988).
On epilepsy: investigations on the level of the nerve membrane and of the brain.
PhD thesis, University of Leiden, Leiden, The Netherlands.

van Neerven, 1987
van Neerven, J. (1987).
Determination of the correlation dimension from a time series.
Master's thesis, Universiteit van Amsterdam, Amsterdam, The Netherlands.

W.L. Deemer, Jr. and D.F. Votaw, Jr., 1955
W.L. Deemer, Jr. and D.F. Votaw, Jr. (1955).
Estimation of parameters of truncated or censored exponential distributions.
Ann. Math. Statist., 26:498.

Wolf et al., 1985
Wolf, A., Swift, J., Swinney, H., and Vastano, J. (1985).
Determining lyapunov exponents from a time series.
Physica, 16D:285.