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Problems on Self-similar Geometry

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Fractal Geometry and Stochastics II

Part of the book series: Progress in Probability ((PRPR,volume 46))

Abstract

Abstract. We discuss some results and open questions in the field of classical self-similar constructions: Boundaries of self-similar sets with open set condition; the dimension of a self-similar set with a big overlapping; the singularity of self-similar measures with respect to Hausdorff and packing measures and a variational property of self-similar measures which plays a role in multifractality. The multidimensional Legendre Transform is shown to satisfy the multifractal formalism for intersections of several multifractal layers relative to different self-similar measures.

The research in this paper has been partially supported by DGES, PB97-0301.

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Author information

Authors and Affiliations

  1. Departamento de Analisis Economico I, Universidad Complutense de Madrid, Campus de Somosaguas, 28223, Madrid

    Manuel Moran

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  1. Manuel Moran
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Editors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, 17487, Germany

    Christoph Bandt

  2. Fakultät für Mathematik und Informatik, Universität Passau, Passau, 94030, Germany

    Siegfried Graf

  3. Mathematisches Institut, Friedrich-Schiller-Universität, Jena, 07740, Germany

    Martina Zähle

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© 2000 Springer Basel AG

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Moran, M. (2000). Problems on Self-similar Geometry. In: Bandt, C., Graf, S., Zähle, M. (eds) Fractal Geometry and Stochastics II. Progress in Probability, vol 46. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8380-1_3

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  • DOI: https://doi.org/10.1007/978-3-0348-8380-1_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9542-2

  • Online ISBN: 978-3-0348-8380-1

  • eBook Packages: Springer Book Archive

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