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Projections of Self-Similar and Related Fractals: A Survey of Recent Developments

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Fractal Geometry and Stochastics V

Part of the book series: Progress in Probability ((PRPR,volume 70))

Abstract

In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand’s Theorem, and quantify the size of every projection – or at least every projection outside some very small set. This article surveys some of these results and the techniques that were developed to obtain them, focusing on linear projections of planar self-similar sets and measures.

The author was partially supported by Projects PICT 2011-0436 and PICT 2013-1393 (ANPCyT) http://www.utdt.edu/profesores/pshmerkin

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Torcuato Di Tella University, and CONICET, Buenos Aires, Argentina

    Pablo Shmerkin

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  1. Pablo Shmerkin
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Correspondence to Pablo Shmerkin .

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Editors and Affiliations

  1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

    Christoph Bandt

  2. Mathematical Institute, University of St Andrews, St Andrews, United Kingdom

    Kenneth Falconer

  3. Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Martina Zähle

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Shmerkin, P. (2015). Projections of Self-Similar and Related Fractals: A Survey of Recent Developments. In: Bandt, C., Falconer, K., Zähle, M. (eds) Fractal Geometry and Stochastics V. Progress in Probability, vol 70. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18660-3_4

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