250109 VO Ergodic Theory (2017S)
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Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
First class on March 7.
Tuesday
07.03.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
07.03.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
14.03.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
14.03.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
21.03.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
21.03.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
28.03.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
28.03.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
04.04.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
04.04.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
25.04.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
25.04.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
02.05.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
02.05.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
09.05.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
09.05.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
16.05.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
16.05.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
23.05.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
23.05.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
30.05.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
30.05.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
13.06.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
13.06.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
20.06.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
20.06.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
27.06.
14:15 - 15:00
Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday
27.06.
16:45 - 17:30
Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
This is a general introduction to Ergodic Theory, communicated by lectures.
Assessment and permitted materials
Oral Exam.
Minimum requirements and assessment criteria
Broad and general understanding of the topics covered in this course.
Examination topics
Core material:
- Invariant measures, Krylov-Bogul'jubov Theorem.
- Absolute continuity, densities (= Radon-Nikodym derivative)
- Basic examples of measure preserving transformations (circle rotation, - doubling map, full shift)
- Ergodicity and unique ergodicity.
- Birkhoff's Ergodic Theorem and basic applications.
- Poincare's Recurrence Theorem, Kac's Lemma.
- Mixing and weak mixing, their characterization and relation.
- Invariant measures, Krylov-Bogul'jubov Theorem.
- Absolute continuity, densities (= Radon-Nikodym derivative)
- Basic examples of measure preserving transformations (circle rotation, - doubling map, full shift)
- Ergodicity and unique ergodicity.
- Birkhoff's Ergodic Theorem and basic applications.
- Poincare's Recurrence Theorem, Kac's Lemma.
- Mixing and weak mixing, their characterization and relation.
Reading list
- Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975
ISBN 0-387-95152-0.
- Karl Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, 1983, Cambridge University Press ISBN 0-521-38997-6
- Michael Brin and Garrett Stuck,
Introduction to Dynamical Systems, Cambridge University Press 2002, ISBN 0-521-80841-3
ISBN 0-387-95152-0.
- Karl Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, 1983, Cambridge University Press ISBN 0-521-38997-6
- Michael Brin and Garrett Stuck,
Introduction to Dynamical Systems, Cambridge University Press 2002, ISBN 0-521-80841-3
Association in the course directory
MSTV
Last modified: Mo 07.09.2020 15:40