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Fractal Geometry and Analysis

  • Jacques Bélair
  • Serge Dubuc

Part of the NATO ASI Series book series (ASIC, volume 346)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Paul Blanchard, Amy Chiu
    Pages 45-98
  3. Serge Dubuc
    Pages 121-220
  4. Kenneth J. Falconer
    Pages 221-254
  5. Michel Mendès France
    Pages 325-366
  6. Claude Tricot
    Pages 367-403
  7. Back Matter
    Pages 469-472

About this book

Introduction

This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy­ namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.

Keywords

Branching process calculus dynamical systems dynamische Systeme geometry systems theory

Editors and affiliations

  • Jacques Bélair
    • 1
  • Serge Dubuc
    • 1
  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-7931-5
  • Copyright Information Springer Science+Business Media B.V. 1991
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-015-7933-9
  • Online ISBN 978-94-015-7931-5
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site