Universität Wien
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250410 VO Selected topics in ergodic theory (2007S)

Selected topics in ergodic theory

6.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Vorbesprechung am Mittwoch, 7. März 2007, 11.00 Uhr,
C 209 (UZA 4)

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 21.03. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 28.03. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 18.04. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 25.04. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 02.05. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 09.05. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 16.05. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 23.05. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 30.05. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 06.06. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 13.06. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 20.06. 10:00 - 12:00 (ehem. Seminarraum A 1.01)
  • Wednesday 27.06. 10:00 - 12:00 (ehem. Seminarraum A 1.01)

Information

Aims, contents and method of the course

The aim of this course is an introduction into two areas of current research:

1. Symbolic representation of dynamical systems: Isomorphisms und equivariant maps between shift-spaces and dynamical systems which are generated by automorphisms of compact abelian groups.
Topics:
(a) Vershik's algebraic construction of Markov partitions for hyperbolic automorphisms of the n-dimensional torus and its extensions to quasihyperbolic automorphisms and algebraic Zd-actions,
(b) Symbolic covers of algebraic Zd-actions, in particular connections between dimer models and the 'sandpile models' of statistical mechanics and 'harmonic algebraic Zd-actions.

2. Ratner's theorem about invariant measures of unipotent flows on homogeneous spaces.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Eine gute Einführung in die Thematik gibt es in Chapter 13 auf http://www.mth.uea.ac.uk/ergodic/

Association in the course directory

Last modified: Mo 07.09.2020 15:40