Universität Wien

250109 VO Ergodic Theory (2017S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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.

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

Association in the course directory

MSTV

Last modified: Mo 07.09.2020 15:40