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250109 VO Ergodic Theory (2025S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Mo 03.03. 09:45-11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Lecturers

Roland Zweimüller

Classes (iCal) - next class is marked with N

N Monday 03.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 04.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 11.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 17.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 18.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 24.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 25.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 31.03. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 01.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.04. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 08.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 28.04. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 29.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 05.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 06.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 12.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 13.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 19.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 20.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 26.05. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 27.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 02.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 03.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 10.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 16.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 17.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 23.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 24.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 30.06. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Ergodic Theory is a multi-faceted field of mathematics. The goal of this course is to explain how it allows us to understand (important features of) the long-term behavior of dynamical systems which are "chaotic" in that detailed predictions are impossible (for mathematical reasons). This is a "quantitative" (measure-theoretic) study of dynamical systems complementing the "qualitative" (topological) viewpoint often discussed in courses on differential equations. While everything will be illustrated in the context of simple prototypical examples, the basic theory takes place in an abstract measure-theoretic setup, and a background in (or the willingness to learn some) functional analysis and probability theory is also useful. Interested students can also register for 250107-1 SE Seminar Stochastics and Dynamics (2025S), where it is possible to delve even deeper into topics related to the present course, based on the participant's individual preferences.
[Keywords: measurable dynamical systems, recurrence, ergodicity, invariant measures, ergodic theorems, entropy, stochastic properties.]

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

understanding and working knowledge of the material discussed in the lectures

Examination topics

will be specified during the lectures

Reading list