(in Polish) Introduction to topological dynamics
7404-MAT-TOP-INTRO
1. Basic concepts of topological dynamics: orbit, invariant set, topological dynamical system, factor, extension, recurrence, minimal set.
2. Birkhoff's recurrence theorem and topological van der Waerden' theorem.
3. Combinatorial conclusions from recurrence theorems.
4. Cantor space and Cech-Stone compactification of the set of natural numbers.
Total student workload
30 hours - lecture
30 hours - preparing for classes and studying literature
30 hours - preparation for the exam
Total: 90 hours
Learning outcomes - knowledge
After completing the course, the doctoral student:
W1: Understands the concept of a topological dynamical system
W2. Knows examples of topological dynamical systems
W3. Knows the recurrence theorems and their combinatorial conclusions
W4: Understands the Cech-Stone compactification of the set of natural numbers
(P8S_WG)
Learning outcomes - skills
After completing the course, the doctoral student:
U1: Is able to indicate the differences between the properties of known topological dynamical systems
U2: Uses advanced methods of topological dynamics
U3: Is able to describe factors and extensions of known topological dynamical systems
(P8S_UW)
Learning outcomes - social competencies
After completing the course, the doctoral student:
1. Passes on his knowledge and thoughts to others while maintaining intellectual honesty. (P8S_KR, P8S_KK)
2. Is aware of the limitations of his knowledge, has the ability to critically look at the issue under consideration and is able to look for solutions based on the principles of logic and various sources of information. (P8S_KK)
Teaching methods
lecture in traditional form
Expository teaching methods
- informative (conventional) lecture
Course coordinators
Assessment criteria
Bibliography
D. Ellis, R. Ellis, Automorphisms and Equivalence Relations in Topological Dynamics
S. Geschke, Topological dynamics
D. Lind, B. Marcus, An Introduction to Symbolic Dynamics and Coding
T. Tao, What's new, blog
P. Walters, An Introduction to Ergodic Theory
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: