Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Introduction to Fractal Geometry
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.
Professor Lars Aake Andersson
Lecturer
Sze Man Ngai
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.
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
Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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