▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Analysis F
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kawahira Tomoki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(H119A)
- Group
- -
- Course number
- MTH.C502
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 2Q
- Syllabus updated
- 2016/4/27
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
"The Beltrami equation" is a partial differential equation whose homeomorphic solutions realize a given deformation of (1 dimensional) complex structure in terms of the "Beltrami coefficient". When the norm of "the Beltrami coefficient" is strictly less than one, its homeomorphic solution is called a "quasiconformal mapping", which is an essential tool for the theories of Teichmullar space, Kleinian groups, and complex dynamics. In this course we will start with several solutions Beltrami equations, then we will learn some basics on complex dynamics and significant applications of quasiconformal mappings. This course is a succession of "Advanced Topics in Analysis E" in the previous quarter.
The students will learn some remarkable applications of the Beltrami equations and quasifoncormal mappings in the theory of complex dynamics.
Student learning outcomes
At the end of this course, students are expected to:
-- be familiar with some basics of complex dynamics.
-- understand the principle of quasiconformal perturbation and quasiconformal surgery
Keywords
Beltrami coefficient, Beltrami Equation，quasiconformal mappings, complex dynamics, Julia sets, Fatou sets
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. Homework will be assigned occasionally
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Classification of stable domains in complex dynamics | Details will be provided in class. |
| Class 2 | Fatou-Shishikura inequality 1 | |
| Class 3 | Fatou-Shishikura inequality 2 | |
| Class 4 | Polynomial-like mappings and traightening | |
| Class 5 | Sullivan's no wandering domain theorem 1 | |
| Class 6 | Sullivan's no wandering domain theorem 1 | |
| Class 7 | Degenerate Beltrami equations of David class | |
| Class 8 | Parabolic surgery, an application of degenerate Beltrami equations of David class |
Textbook(s)
None required
Reference books, course materials, etc.
Ahlfors, "Lectures on Quasifoncormal mappings"
Carleson-Gamelin, "Complex Dynamics", Springer
Beardon, "Complex Dynamics", Springer
Assessment criteria and methods
assignments 100%.
Related courses
- MTH.C501 ： Advanced topics in Analysis E
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None required
