Universität Wien

442503 VO Selected Topics in Dynamics (2017S)

3.00 ECTS (2.00 SWS), SPL 44 - Doktoratsstudium Naturwissenschaften und technische Wissenschaften

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 07.03. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.03. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.03. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.03. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 04.04. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.04. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 02.05. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.05. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.05. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.05. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.05. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.06. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 20.06. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 27.06. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course is meant as introduction to symbolic dynamic,
which serves as symbolic coding of dynamical systems, but also has its own status, with connections to computability and formal automata.
The course will be based on lectures only.

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Broad and general understanding of the topics covered in this course.

Examination topics

Among the topics likely to be discussed are:
- Language and (sub)shift spaces: basic notions and definitions.
- Subshifts of finite type and sofic subshifts; equivalence between subshifts.
- Automata approach and Turing machines
- Linguistic complexity and the Chomsky hierarchy.
- Entropy and word-complexity
- minimal subshifts; uniform and linear recurrence.
- Sturmian subshifts
- Substitution subshifts and Toeplitz subshifts.
- Bratteli diagrams and the Vership map
- Subshifts coming from one-dimensional
dynamics (\beta-transformation, kneading theory).
- Cellular automata.

Reading list

- Bruce Kitchens, Symbolic dynamics: one-sided, two-sided and countable state Markov shifts, Springer Verlag. ISBN 3-540 -62738-3
-Douglas & Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge Univ Press, ISBN 0-521-55900-6
- Martine Queffélec, Substitution dynamical systems and spectral analysis, Lect. Notes in Math 1294, Springer-Verlag. ISBN 3-540-18692-1.
-John Hopcroft and Jeffrey Ullman, Introduction to Automata Theory, Languages and Computation, Addision-Wesley Publ. ISBN 0-201-02988-X

Association in the course directory

MSTV

Last modified: Mo 07.09.2020 15:47