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A Short Existence Proof for Correlation Dimension

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Abstract

The Grassberger–Hentschel–Procaccia correlation dimension has been put on a rigorous basis by Pesin and Tempelman. We simplify their proof that this dimension is given in terms of the measure of neighborhoods of the diagonal.

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REFERENCES

  1. Ya. Pesin, On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions. J. Stat. Phys. 71:529-547 (1993).

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  2. Ya. Pesin and A. Tempelman, Correlation dimension of measures invariant under group actions, Random & Computational Dynamics 3:137-156 (1995).

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  3. I. Procaccia, P. Grassberger, and V. G. E. Hentschel, On the characterization of chaotic motions, in Lecture notes in Physics, no. 179 (Springer, Berlin, 1983), pp. 212-221.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K

    Anthony Manning

  2. Institute of Mathematics, University of Miskolc, Miskolc-Egyetemváros, H-3515, Hungary

    Károly Simon

Authors
  1. Anthony Manning
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  2. Károly Simon
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Manning, A., Simon, K. A Short Existence Proof for Correlation Dimension. Journal of Statistical Physics 90, 1047–1049 (1998). https://doi.org/10.1023/A:1023253709865

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  • DOI: https://doi.org/10.1023/A:1023253709865

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