Description

Book Synopsis
While there is no precise definition of a fractal, it is usually understood as a set whose smaller parts when magnified resemble the whole. Suitable for a wide audience of mathematicians, this book is devoted to self-similar and self-affine sets, for which this resemblance is precise and given by a contracting similitude or affine transformation.

Table of Contents
  • Introduction
  • Elements of geometric measure theory
  • General properties of self-similar sets and measures
  • Separation properties for self-similar IFS
  • Multifractal analysis for self-similar measures
  • Transversality techniques for self-similar IFS
  • Further properties of self-similar IFS with overlaps
  • Fourier-analytic and number-theoretic methods
  • Elements of ergodic theory
  • Self-affine sets and measures
  • Diagonally self-affine IFS
  • Exact dimensionality and dimension conservation
  • Local entropy averages and projections of self-affine sets and measures
  • Nonlinear conformal iterated functions systems
  • Some elements of linear algebras
  • Some elements of measure theory
  • Some elements of harmonic analysis
  • Some acts about algebraic numbers
  • Bibliography
  • Index
  • Basic notation

Selfsimilar and Selfaffine Sets and Measures

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    £103.50

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    RRP £115.00 – you save £11.50 (10%)

    Order before 4pm today for delivery by Tue 23 Jun 2026.

    A Paperback by Balazs Barany, Karoly Simon, Boris Solomyak

    3 in stock


      View other formats and editions of Selfsimilar and Selfaffine Sets and Measures by Balazs Barany

      Publisher: MP-AMM American Mathematical
      Publication Date: 12/30/2023 12:00:00 AM
      ISBN13: 9781470470463, 978-1470470463
      ISBN10: 1470470462

      Description

      Book Synopsis
      While there is no precise definition of a fractal, it is usually understood as a set whose smaller parts when magnified resemble the whole. Suitable for a wide audience of mathematicians, this book is devoted to self-similar and self-affine sets, for which this resemblance is precise and given by a contracting similitude or affine transformation.

      Table of Contents
      • Introduction
      • Elements of geometric measure theory
      • General properties of self-similar sets and measures
      • Separation properties for self-similar IFS
      • Multifractal analysis for self-similar measures
      • Transversality techniques for self-similar IFS
      • Further properties of self-similar IFS with overlaps
      • Fourier-analytic and number-theoretic methods
      • Elements of ergodic theory
      • Self-affine sets and measures
      • Diagonally self-affine IFS
      • Exact dimensionality and dimension conservation
      • Local entropy averages and projections of self-affine sets and measures
      • Nonlinear conformal iterated functions systems
      • Some elements of linear algebras
      • Some elements of measure theory
      • Some elements of harmonic analysis
      • Some acts about algebraic numbers
      • Bibliography
      • Index
      • Basic notation

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