401-3372-00L Dynamical Systems II
Semester | Spring Semester 2020 |
Lecturers | W. Merry |
Periodicity | non-recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|
401-3372-00 V | Dynamical Systems II | 4 hrs |
| W. Merry | ||||||
401-3372-00 U | Dynamical Systems II | 1 hrs |
| W. Merry |
Catalogue data
Abstract | This course is a continuation of Dynamical Systems I. This time the emphasis is on hyperbolic and complex dynamics. |
Learning objective | Mastery of the basic methods and principal themes of some aspects of hyperbolic and complex dynamical systems. |
Content | Topics covered include: - Hyperbolic linear dynamical systems, hyperbolic fixed points, the Hartman-Grobman Theorem. - Hyperbolic sets, Anosov diffeomorphisms. - The (Un)stable Manifold Theorem. - Shadowing Lemmas and stability. - The Lambda Lemma. - Transverse homoclinic points, horseshoes, and chaos. - Complex dynamics of rational maps on the Riemann sphere - Julia sets and Fatou sets. - Fractals and the Mandelbrot set. |
Lecture notes | I will provide full lecture notes, available here: https://www.merry.io/courses/dynamical-systems/ |
Literature | The most useful textbook is - Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002. |
Prerequisites / Notice | It will be assumed you are familiar with the material from Dynamical Systems I. Full lecture notes for this course are available here: https://www.merry.io/courses/dynamical-systems/ However we will only really use material covered in the first 10 lectures of Dynamical Systems I, so if you did not attend Dynamical Systems I, it is sufficient to read through the notes from the first 10 lectures. In addition, it would be useful to have some familiarity with basic differential geometry and complex analysis. |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
![]() | |
ECTS credits | 10 credits |
Examiners | W. Merry |
Type | session examination |
Language of examination | English |
Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
Mode of examination | written 180 minutes |
Additional information on mode of examination | Offered in the summer examination session 2020 and in the winter examination session 2020/21. Be aware that no further examination might be offered until this non-recurring course will be offered again. |
Written aids | None |
This information can be updated until the beginning of the semester; information on the examination timetable is binding. |
Learning materials
No public learning materials available. | |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |
Offered in
Programme | Section | Type | |
---|---|---|---|
Mathematics Bachelor | Core Courses: Pure Mathematics | W | ![]() |
Mathematics Master | Core Courses: Pure Mathematics | W | ![]() |