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Editorial Reviews
Review
Peter R. Massopust, "Mathematical Reviews" Mathematical Reviews : Well
written and accessible to undergraduates or anybody who would like to
obtain a quick but well-rounded introduction to fractal analysis. It is
highly recommended and will certainly find a well-deserving place on
many bookshelves.
Book Description
Differential Equations on Fractals opens the door to understanding the
recently developed area of analysis on fractals, focusing on the
construction of a Laplacian on the Sierpinski gasket and related
fractals. Written in a lively and informal style, with lots of
intriguing exercises on all levels of difficulty, the book is accessible
to advanced undergraduates, graduate students, and mathematicians who
seek an understanding of analysis on fractals. Robert Strichartz takes
the reader to the frontiers of research, starting with carefully
motivated examples and constructions.
One of the great accomplishments of geometric analysis in the nineteenth
and twentieth centuries was the development of the theory of Laplacians
on smooth manifolds. But what happens when the underlying space is
rough? Fractals provide models of rough spaces that nevertheless have a
strong structure, specifically self-similarity. Exploiting this
structure, researchers in probability theory in the 1980s were able to
prove the existence of Brownian motion, and therefore of a Laplacian, on
certain fractals. An explicit analytic construction was provided in 1989
by Jun Kigami. Differential Equations on Fractals explains Kigami's
construction, shows why it is natural and important, and unfolds many of
the interesting consequences that have recently been discovered.
This book can be used as a self-study guide for students interested in
fractal analysis, or as a textbook for a special topics course.
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