Fractal Geometry and Stochastics (Progress in Probability, 37) 1995th Edition by Christoph Bandt (PDF)

Description

Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference “Fractal Geometry and Stochastics” held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very nice collection of papers: tutorials, and well written research presented to a wide audience. They cover stochastic aspects, geometry, analysis, iterated function systems, algorithms, to mention just a few. And they are written by authorities in the field. Fractals make headlines from time to time[–are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an exciting mathematical history. This very important book presents the subject in a way that it can be taught to students. Or it can be used for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. A recent example of this: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The authors have produced an attractive book on fractals. There are others, for example one by Falconer from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

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