Universität Wien

442502 VO Ergodic theory II (2014W)

5.00 ECTS (3.00 SWS), SPL 44 - Doktoratsstudium Naturwissenschaften und technische Wissenschaften

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

First lecture on Wednesday October 1st

  • Wednesday 01.10. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.10. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.10. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.10. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.10. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.10. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.10. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.10. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.10. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.10. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.11. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 06.11. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.11. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.11. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.11. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.11. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.11. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.11. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.12. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.12. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.12. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.12. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.12. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.12. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.01. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.01. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.01. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.01. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.01. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.01. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.01. 14:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 29.01. 14:00 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course goes deeper into ergodic theory, with main content: the theory of entropy and methods of thermodynamic formalism. Topics to be discussed are likely to include
- Definition and properties of entropy (both topological and metric). The variational principle.
- Entropy as invariant under isomorphism, and complete invariant under isomorphism for Bernoulli shifts.
- Basic notions and motivation of thermodynamic formalism.
- Applications of thermodynamic formalism to (fractal) dimension theory. Dimension formulas.
- Entropy and pressure for induced transformations (Abramov's formula).

Assessment and permitted materials

Oral exam (in Englisch or German depending on student's preference).

Minimum requirements and assessment criteria

Examination topics

Lecture + course material on website

Reading list

Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag 1975
ISBN 0-387-95152-0.
Gerhard Keller, Equilibrium States in Ergodic Theory, Cambridge Univ. Press. 1998.
Omri Sarig, Lecture Notes on Thermodynamic Formalism for Topological Markov Shifts. Penn State, 2009.

Association in the course directory

MSTV

Last modified: Mo 07.09.2020 15:47