Hausdorff dimension and uniformity factor of strange attractors

Details Hausdorff dimension and uniformity factor of strange attractors Hausdorff dimension and uniformity factor of strange attractors

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984phrvl..52.1661b&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 52, May 7, 1984, p. 1661-1664.

Physics

80

Fractals, Strange Attractors, Algorithms, Balls, Dimensions

Scientific paper

The Hausdorff dimension of a strange attractor is argued to be the fixed point of a recursive relation, defined in terms of a suitable average of the smallest distances between points on the attractor. A fast numerical algorithm is developed to compute the Hausdorff dimension. The spread in the convergence rates towards zero of the distances between points on the attractor (uniformity factor) as well as the stability of the fixed point are discussed in terms of the entropy of the distribution of the smallest distances between points on the attractor.

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