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Benoit Mandelbrot
NEGATIVE FRACTAL DIMENSION
Negative Holding and Divergent Moments
VIRTUAL SELECTA
This open-ended virtual book will be compiled
and extended as needs and opportunities arise.
It consists in links to the author’s
publications on negative fractal dimension
that are found on this home site
http://www.math.yale.edu/mandelbrot
TABLE OF CONTENTS
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123 |
WWW M. M 1989e. A class of multifractal measures
with negative (latent) values for the “dimension” f(a)).
Fractals’ Physical Origin and Properties (Erice,
1988). Edited by Luciano Pietronero, New York: Plenum, 3-29.
• Short version: Negative fractal dimensions and multifractals.
Statistical Physics 17, International IUPAP Conference
(Rio de Janeiro, 1989). Edited by Constantino Tsallis, Physica:
A163, 1990, 306-315.
[ PDF
(3.53 MB) ]
• Updated short version: Two meanings of multifractality,
and the notion of negative fractal dimension. Chaos/Xaoc: Soviet-American
Perspectives on Nonlinear Science (Woods Hole, 1989). Edited
by David K. Campbell. New York: American Institute of Physics, 1990,
79-90.
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124 |
WWW M. M 1990t. Limit lognormal multifractal measures.
Frontiers of Physics: Landau Memorial Conference (Tel Aviv,
1988). Edited by E. A. Gotsman et al. New York: Pergamon, 309-340.
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130 |
WWW M. M 1991k. Random multifractals: negative
dimensions and the resulting limitations of the thermodynamic formalism.
Proceedings of the Royal Society (London): A434,
79-88. Also in Turbulence and Stochastic Processes: Kolmogorov’s
ideas 50 years on. Edited by Julian C. R. Hunt, O. M. Phillips,
& D. Williams, London: The Royal Society.
[ PDF
(2.92 MB) ]
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150 |
WWW M. M 1995k. Negative dimensions and Hölder,
multifractals and their Hölder spectra, and the role of lateral
preasymptotics in science. J. P. Kahane meeting (Paris, 1993).
Edited by Aline Bonami & Jacques Peyrière. The Journal
of Fourier Analysis and Applications: special issue, 409-432.
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179 |
WWW M. M 2003f. Multifractal power-law distributions,
other “anomalies,” and critical dimensions, explained
by a simple example. Journal of Statistical Physics: 110,
739-777.
[ PDF
(451 KB) ]
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180 |
WWW P. M 2003r. Heavy tails in finance for independent
or multifractal price increments. Handbook on Heavy Tailed Distributions
in Finance. Edited by Svetlozar T. Rachev (Handbooks in Finance:
30, Senior Editor: William T. Ziemba): 1,
1-34.
[ PDF
(295.1 KB) ]
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