Universität Wien

250411 VO Ergodic theory (2008S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 05.03. 09:00 - 11:00 Seminarraum
  • Thursday 06.03. 09:00 - 11:00 Seminarraum
  • Wednesday 12.03. 09:00 - 11:00 Seminarraum
  • Thursday 13.03. 09:00 - 11:00 Seminarraum
  • Wednesday 19.03. 09:00 - 11:00 Seminarraum
  • Thursday 20.03. 09:00 - 11:00 Seminarraum
  • Wednesday 26.03. 09:00 - 11:00 Seminarraum
  • Thursday 27.03. 09:00 - 11:00 Seminarraum
  • Wednesday 02.04. 09:00 - 11:00 Seminarraum
  • Thursday 03.04. 09:00 - 11:00 Seminarraum
  • Wednesday 09.04. 09:00 - 11:00 Seminarraum
  • Thursday 10.04. 09:00 - 11:00 Seminarraum
  • Wednesday 16.04. 09:00 - 11:00 Seminarraum
  • Thursday 17.04. 09:00 - 11:00 Seminarraum
  • Wednesday 23.04. 09:00 - 11:00 Seminarraum
  • Thursday 24.04. 09:00 - 11:00 Seminarraum
  • Wednesday 30.04. 09:00 - 11:00 Seminarraum
  • Wednesday 07.05. 09:00 - 11:00 Seminarraum
  • Thursday 08.05. 09:00 - 11:00 Seminarraum
  • Wednesday 14.05. 09:00 - 11:00 Seminarraum
  • Thursday 15.05. 09:00 - 11:00 Seminarraum
  • Wednesday 21.05. 09:00 - 11:00 Seminarraum
  • Wednesday 28.05. 09:00 - 11:00 Seminarraum
  • Thursday 29.05. 09:00 - 11:00 Seminarraum
  • Wednesday 04.06. 09:00 - 11:00 Seminarraum
  • Thursday 05.06. 09:00 - 11:00 Seminarraum
  • Wednesday 11.06. 09:00 - 11:00 Seminarraum
  • Thursday 12.06. 09:00 - 11:00 Seminarraum
  • Wednesday 18.06. 09:00 - 11:00 Seminarraum
  • Thursday 19.06. 09:00 - 11:00 Seminarraum
  • Wednesday 25.06. 09:00 - 11:00 Seminarraum
  • Thursday 26.06. 09:00 - 11:00 Seminarraum

Information

Aims, contents and method of the course

In the simplest setting a dynamical system consists of a measure space, a topological space or a smooth manifold, and of one or more
transformations of the space which preserve its structure (i.e. of measure-preserving transformations, homeomorphisms of diffeomorphisms). The mathematical theory of such systems focuses on the asymptotic properties and complexity of the orbits of these
transformations (in applied dynamics a certain degree of this complexity is sometimes called "chaos"). Depending on whether one is
in a measure-theoretic, topological or smooth setting one speaks of "Ergodic Theory", "Topological Dynamics" or "Smooth Dynamics".

An important class of dynamical systems arise from stationary stochastic processes in probability theory (e.g. Markov processes). Other classes of examples come from number theory (uniform
distribution, digit expansions, continued fractions) or from algebra (e.g. toral automorphism).

This course will mostly focus on ergodic theory, but some topics from topological dynamics will also be discussed.

Some special topics:

Examples of dynamical systems

Uniform distribution and topological dynamics

Recurrence and the principal ergodic theorems

Mixing properties

Spectral properties

Information and entropy

hyperbolic dynamical systems

Assessment and permitted materials

Minimum requirements and assessment criteria

This lecture course offers an introduction to ergodic theory and topological dynamics, leading up to problems in current research.

Examination topics

Lecture course

Reading list

A. Katok und B. Hasselblatt: Introduction to the modern theory of dynamical systems, Cambridge, 1995

W. Parry, Topics in ergodic theory, Cambridge University Press, Cambridge, 1981.

K. Petersen, Ergodic theory, Cambridge University Press, Cambridge, 1983.

P. Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, vol. 79, Springer Verlag, Berlin-Heidelberg-New York, 1982.

Association in the course directory

MSTV

Last modified: Mo 07.09.2020 15:40