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Self-Similarity, L p-Spectrum and Multifractal Formalism

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Fractal Geometry and Stochastics

Part of the book series: Progress in Probability ((PRPR,volume 37))

Abstract

This is an expository survey of recent work on self-similar measures centered around the L p-spectrum and its relationship to the local dimension spectrum. The relationship is the multifractal formalism proposed by physicists. We will treat the formalism rigorously here. The open set condition and a new weaker separation condition will be discussed in detail; several techniques for calculating the L p-spectrum will be introduced; and the multifractal structure of functions satisfying the two-scale dilation equations will also be discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, 15260, USA

    Ka-Sing Lau

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  1. Ka-Sing Lau
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Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, D-17487, Greifswald, Deutschland

    Christoph Bandt

  2. Fakultät für Mathematik und Informatik, Universität Passau, D-94030, Passau, Deutschland

    Siegfried Graf

  3. Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, D-07740, Jena, Deutschland

    Martina Zähle

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Lau, KS. (1995). Self-Similarity, L p-Spectrum and Multifractal Formalism. In: Bandt, C., Graf, S., Zähle, M. (eds) Fractal Geometry and Stochastics. Progress in Probability, vol 37. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7755-8_4

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  • DOI: https://doi.org/10.1007/978-3-0348-7755-8_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7757-2

  • Online ISBN: 978-3-0348-7755-8

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