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About this book
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.
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Editors and Affiliations
Bibliographic Information
Book Title: Fractal Geometry and Analysis
Editors: Jacques Bélair, Serge Dubuc
Series Title: Nato Science Series C:
DOI: https://doi.org/10.1007/978-94-015-7931-5
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1991
Hardcover ISBN: 978-0-7923-1399-1Due: 31 August 1991
Softcover ISBN: 978-94-015-7933-9Published: 13 November 2013
eBook ISBN: 978-94-015-7931-5Published: 11 November 2013
Series ISSN: 1389-2185
Edition Number: 1
Number of Pages: XV, 472
Number of Illustrations: 85 b/w illustrations
Topics: Measure and Integration, Mathematical Modeling and Industrial Mathematics, Functions of a Complex Variable, Probability Theory and Stochastic Processes