DE

Modul

Ergodic Theory [M-MATH-106473]

Credits
8
Recurrence
Unregelmäßig
Duration
1 Semester
Language
German
Level
4
Version
1

Responsible

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