VO Special Topics in Stochastics: Symbolic Dynamic (2019W.25050.1)

Lecturer: Prof. Henk Bruin

Email H. Bruin for further information for this course.


No lecture on Tuesday December 9.


Day Time Room fromuntil
Tuesday 16:45-18:15 SR09 Lecture10.2.201928.1.2020

Contents 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. 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 Vershik map
- Subshifts coming from one-dimensional dynamics (β-transformation, kneading theory).
- Cellular automata.

The course will be given in English

References/Background reading


Will be based on an oral exam (in English by default, aber auf Deutsch ist auch möglich ).


Course material (Hand-outs)

Updated September 26 2019