Universität Wien
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250095 VO Ergodic theory 1 (2014S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 03.03. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.03. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.03. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.03. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.03. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.03. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.03. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.03. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.04. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.04. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.04. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.04. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.04. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.05. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.05. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.05. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.05. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.05. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.05. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.05. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.05. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.06. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.06. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.06. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.06. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.06. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.06. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.06. 16:00 - 17:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.06. 13:00 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is an introduction to ergodic theory, that is: the study of how invariant measures play a role in dynamical systems.

Topics to be discussed are likely to include
- Invariant measures in various standard examples (both finite and infinite);
- Ergodicity, unique ergodicity and proving ergodicity;
- Poincare recurrence and Kac' Lemma;
- Ergodic Theorems, Chacon-Ornstein Theorem and similar results;
- Induced transformations, Rokhlin towers and similar results;
- Transfer operators;
- Connections to notions from Probability Theory (Mixing, Bernoulli processes).

Assessment and permitted materials

Assessment is based on an oral exam.

Minimum requirements and assessment criteria

See course description

Examination topics

Lectures

Reading list

- Peter Walters, An Introduction to Ergodic Theory,
Springer-Verlag 1975 ISBN 0-387-95152-0.

- Ricardo Mañé, Ergodic theory and differentiable dynamics,
Ergebnisse der Mathematik und ihrer Grenzgebiete 8.
Springer-Verlag, Berlin, 1987. ISBN: 3-540-15278-4

- Daniel Rudolph, Fundamentals of measurable dynamics, Oxford Science Publications,
Clarendon Press Oxford 1990 ISBN 0-19-853572-4

- Karl Petersen, Ergodic Theory,
Cambridge Studies in Advanced Mathematics, 1983,
Cambridge University Press ISBN 0-521-38997-6

- Omri Sarig, Lecture Notes on Ergodic Theory Penn State, Fall 2008,
http://www.math.psu.edu/sarig/506/ErgodicNotes.pdf

Association in the course directory

MSTV

Last modified: Mo 07.09.2020 15:40