Introduction to Fractal Geometry
Fractals are highly nonsmooth sets that often possess self-similarity, infinite irregularity, and non-integral Hausdorff dimension. They arise naturally in many branches of mathematics, science, and engineering. This is an introductory course on fractals. Topics include Hausdorff measure and dimension, box dimension, iterated function systems, self-similar sets, the collage theorem, the Moran-Hutchinson theorem, self-similar measures, and the multifractal formalism. Finally, a survey on iterated function systems with overlaps will be given; tentatively, topics will be selected from the weak separation property, the finite type condition, infinite Bernoulli convolutions and related results by Solomyak, Hochman, Varju, and others.

Lecturer
Date
10th September ~ 17th December, 2024
Location
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
Tuesday,Thursday | 09:50 - 11:25 | A7-101 | ZOOM 11 | 435 529 7909 | BIMSA |
Prerequisite
Undergraduate analysis
Syllabus
Chapter 1. Introduction and preliminaries
Chapter 2. Hausdorff measure and Hausdorff dimension
Chapter 3. Box dimension
Chapter 4. Some techniques for calculating dimension
Chapter 5. Iterated function systems and self-similar sets
Chapter 6. Applications to encoding images and the collage theorem
Chapter 7. Self-similar measures
Chapter 8. Survey of iterated function systems with overlaps
Homework assignments will be given regularly but will not be collected for grading.
Chapter 2. Hausdorff measure and Hausdorff dimension
Chapter 3. Box dimension
Chapter 4. Some techniques for calculating dimension
Chapter 5. Iterated function systems and self-similar sets
Chapter 6. Applications to encoding images and the collage theorem
Chapter 7. Self-similar measures
Chapter 8. Survey of iterated function systems with overlaps
Homework assignments will be given regularly but will not be collected for grading.
Reference
Kenneth Falconer, Fractal Geometry, Mathematical Foundation and Applications, 3rd ed, Wiley, 2014. ISBN: 978-1-119-94239-9.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
English