On the Multifractal Character of the Lorenz Attractor

Details On the Multifractal Character of the Lorenz Attractor On the Multifractal Character of the Lorenz Attractor

May 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992pthph..87.1107d&link_type=abstract

Progress of Theoretical Physics, Vol. 87, No. 5, pp. 1107-1118

Physics

5

Scientific paper

A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices alpha_{min} and alpha_{max}. The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character.

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