Conducted in
term:
2024/25
ISCED code: 0541
ECTS credits:
unknown
Language:
English
Organized by:
Doctoral School of Exact and Natural Sciences
Ergodic theory 7404-MAT-TEI-INTRO
1. Joinings and the corresponding Markov operators
2. Graph joinings and Halmos-von Neumann theorem
3. Joinings vs factors
Total student workload
30 hours - lecture
30 hours - preparation for lectures and study of literature
30 hours - preparation for exam
Total 90 hours.
3 ECTS pts
Learning outcomes - knowledge
After finishing the course a PhD student should
W1: Understand the notion of a joining of dynamical systems in the language of measures and Markov operators
W2. Know examples of joinings.
W3. Understand the relation between factors and joinings
(P8S_WG)
Learning outcomes - skills
After finishing the course a PhD student should
U1: Explain difference between various classes of dynamical systems from the point of view of joinings.
U2: Be able to use advanced methods of ergodic theory.
U3: Be able to describe joinings / self-joinings of chosen classes of dynamical systems.
(P8S_UW)
Learning outcomes - social competencies
After finishing the course a PhD student should
K1: Exhibits logical reasoning, recognizes gaps in their knowledge, and asks insightful questions that deepen understanding.
K2: Understands the need for continuous improvement.
(P8S_KK)
Teaching methods
Informative (conventional) lecture
Expository teaching methods
- informative (conventional) lecture
Prerequisites
Basic knowledge of measure theory, HIlbert spaces and operaters on such spaces
Course coordinators
Assessment criteria
oral exam
Bibliography
M. Einsiedler, T. Ward, Ergodic theory
P. Walters, An Introduction to Ergodic Theory
K. Dajani, Ch. Kalle, A First Course in Ergodic Theory
E. Glasner, Ergodic theory via joinings
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: