Syllabus
1. Probability (measure-theoretical) dynamical systems, finite-states stationary processes - definitions, examples, ergodicity, isomorfismus of probability dynamical systems, factorization
2. Entropy of the process, entropy of the system, strictly positive entropy - Kolmogorov property
3. Kolmogorov-Sinai theorem on generators, Shannon-McMillan-Breimann theorem
4. Recurrence, Ornstein-Weiss theorem, Lempel-Ziv algorithm for data compression
Annotation
The basic elements of ergodic theory are presented. We mainly focus on entropy and recurrence.
Tight relationship between ergodic theory and the theory of finite-states stationary processes will be presented.