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Lévy Flights and Related Topics in Physics pp 140–149Cite as

Geometric constructions in multifractality formalism

  • Part 2: Mathematical Approaches
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Part of the book series: Lecture Notes in Physics ((LNP,volume 450))

Abstract

We consider two geometrical approaches for the investigation of multifractal properties of both sets and measures, based on the idea, that a multifractal object is a union of monofractal Cantor-like ones. The first “naive” approach uses a notion of a local dimension of a set or a measure, while the second one uses statistics of empty and full elements of partitions of the phase space for different scales.

On leave from Russian Academy of Sciences, Inst. for Information Transmission Problems, Ermolovoy Str. 19, 101447, Moscow, Russia

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Authors and Affiliations

  1. C.N.R.S., Observatoire de Nice, BP 229, 06304, Nice Cedex 4, France

    Michael Blank

Authors
  1. Michael Blank
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Editor information

Micheal F. Shlesinger George M. Zaslavsky Uriel Frisch

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© 1995 Springer-Verlag

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Blank, M. (1995). Geometric constructions in multifractality formalism. In: Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds) Lévy Flights and Related Topics in Physics. Lecture Notes in Physics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59222-9_31

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  • DOI: https://doi.org/10.1007/3-540-59222-9_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59222-8

  • Online ISBN: 978-3-540-49225-2

  • eBook Packages: Springer Book Archive

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