VO Special Topics in Stochastics: Symbolic Dynamic (2019W.25050.1)
Email
H. Bruin
for further information for this course.
Announcements
No lecture on Tuesday December 9.
Schedule
Day  Time  Room   from  until 
Tuesday  16:4518:15  SR09  Lecture  10.2.2019  28.1.2020 
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 wordcomplexity
 Minimal subshifts; uniform and linear recurrence.
 Sturmian subshifts
 Substitution subshifts and Toeplitz subshifts.
 Bratteli diagrams and the Vershik map
 Subshifts coming from onedimensional
dynamics (βtransformation, kneading theory).
 Cellular automata.
The course will be given in English
References/Background reading
 Bruce Kitchens, Symbolic dynamics:
onesided, twosided and countable state Markov shifts,
Springer Verlag. ISBN 3540 627383
 Douglas Lind & Brian Marcus, An introduction to symbolic dynamics and coding,
Cambridge Univ Press, ISBN 0521559006
 Martine Queffélec, Substitution dynamical systems and spectral analysis,
Lect. Notes in Math 1294, SpringerVerlag. ISBN 3540186921.
 John Hopcroft and Jeffrey Ullman,
Introduction to Automata Theory, Languages and Computation,
AddisionWesley Publ. ISBN 020102988X

Topics in Symbolic Dynamics and Applications
London Mathematical Society Lecture Note Series
Editors: F. Blanchard, A. Maass, A. Nogueira,
Cambridge Univ. Press 2000, ISBN 9780521796606
 Notes Karl Petersen's
website
Assessment
Will be based on an oral exam (in English by default, aber auf Deutsch ist auch möglich ).
Material:
 Class notes.
These notes are part of a longer text (still n progress) and therefore some crossreferences are missing (usually indicated by ??).
Course material (Handouts)
Updated September 26 2019