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Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems

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Dimensions and Entropies in Chaotic Systems

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 32))

Abstract

An infinite sequence of moments is needed to describe a fractal measure. This fact is widely known today, largely thanks to several speakers at this conference, who either refer to it, or push well beyond. Here, I propose to sketch the extensive early background in my work (before 1968) on the theory of turbulent intermittency. This old story matters, because my general procedure also brings forward a number of topics that have not been duplicated, and calls attention to interesting open issues.

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References

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Author information

Authors and Affiliations

  1. Physics Department, IBM Research Center, Mathematics Department, Harvard University, Cambridge, MA, 02138, USA

    B. B. Mandelbrot

Authors
  1. B. B. Mandelbrot
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Editor information

Editors and Affiliations

  1. Center for Nonlinear Studies, Los Alamos National Laboratory, Mail Stop: B258, Los Alamos, NM, 87545, USA

    Gottfried Mayer-Kress

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© 1986 Springer-Verlag Berlin Heidelberg

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Mandelbrot, B.B. (1986). Fractal Measures (Their Infinite Moment Sequences and Dimensions) and Multiplicative Chaos: Early Works and Open Problems. In: Mayer-Kress, G. (eds) Dimensions and Entropies in Chaotic Systems. Springer Series in Synergetics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71001-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-71001-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71003-2

  • Online ISBN: 978-3-642-71001-8

  • eBook Packages: Springer Book Archive

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