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Modul
Ergodic Theory [M-MATH-106473]
Credits
8Recurrence
UnregelmäßigDuration
1 SemesterLanguage
GermanLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-113086 | Ergodic Theory | 8 |
Competence Certificate
Oral examination of ca. 20-30 minutes.
Competence Goal
Students
- know important examples of dynamical systems,
- can state and discuss substantial concepts of ergodic theory,
- can state important results on qualitative properties of dynamical systems and relate them,
- are prepared to read recent research articles and write a bachelor or master thesis in the field of ergodic theory.
Prerequisites
None
Content
- Elementary examples of dynamical systems such as Bernoulli systems and billiards
- Poincare rekurrence and ergodic theorems
- mixing, weak mixing, equidistribution
- entropy
- advanced topic(s) (as for example hyperbolic dynamics, symbolic dynamics and coding, Furstenberg correspondence principle or unitary representations of SL(2,R))
Recommendation
Some basic knowledge of measure theory, topology, geometry, group theory and functional analysis is recommended.
Workload
Total workload: 240 hours
Attendance: 90 h
- lectures, problem classes and examination
Self studies: 150 h
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research on the course content,
- preparation for the module examination