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MATH 613 —
Fall 2000
Topics in Analysis: Analysis on Fractals
| Instructor: |
Robert Strichartz |
| Final Time: |
MWF 10:10-11:00 |
Prerequisite: Math 611
Texts:
- Falconer, Fractal Geometry
- Kigami, Analysis on Fractals (xerox)
The first part of the course will cover standard material about fractals
using Falconer's book, including Hausdorff and box dimension, iterated
function systems, self-similar measures, dimensions of measures, multifractal
formalism.
The second part of the course will cover the theory of "fractal differential
equations." Since fractals are not manifolds, there is no standard theory
of differential operators on fractals. Nevertheless, Kigami has constructed
the analog of the Laplacian on a limited class of fractals, including
the familiar Sierpinski gasket. We will describe this construction and
discuss recent research in this area. To get an idea of the subject, see
my expository article in the November 1999 issue of Notices of the AMS.
Last modified:
April 7, 2003
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