401-3372-00L  Dynamical Systems II

SemesterSpring Semester 2020
LecturersW. Merry
Periodicitynon-recurring course
Language of instructionEnglish


401-3372-00 VDynamical Systems II4 hrs
Tue15:15-17:00HG D 1.2 »
Fri10:15-12:00HG D 1.2 »
W. Merry
401-3372-00 UDynamical Systems II1 hrs
Fri12:15-13:00HG D 1.2 »
W. Merry

Catalogue data

AbstractThis course is a continuation of Dynamical Systems I. This time the emphasis is on hyperbolic and complex dynamics.
ObjectiveMastery of the basic methods and principal themes of some aspects of hyperbolic and complex dynamical systems.
ContentTopics 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 notesI will provide full lecture notes, available here:

LiteratureThe most useful textbook is

- Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002.
Prerequisites / NoticeIt will be assumed you are familiar with the material from Dynamical Systems I. Full lecture notes for this course are available here:


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)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersW. Merry
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 180 minutes
Additional information on mode of examinationOffered 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 aidsNone
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.


No information on groups available.


There are no additional restrictions for the registration.

Offered in

Mathematics BachelorCore Courses: Pure MathematicsWInformation
Mathematics MasterCore Courses: Pure MathematicsWInformation