Ergodic Theory - NMTP532
Title: Ergodická teorie
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:3/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://simu0292.utia.cas.cz/seidler/teaching.html
Guarantor: RNDr. Jan Seidler, CSc.
Teacher(s): RNDr. Jan Seidler, CSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Is interchangeable with: NSTP163
Opinion survey results   Examination dates   WS schedule   Noticeboard   
Annotation -
The lectures are devoted to basic properties of measureble dynamical systems, properties like recurrence, ergodicity and mixing being discussed in detail.
Last update: T_KPMS (16.05.2013)
Aim of the course -

Students will learn basic results about measurable dynamical systems.

Last update: T_KPMS (16.05.2013)
Course completion requirements -

Oral exam.

Last update: Zichová Jitka, RNDr., Dr. (13.05.2023)
Literature - Czech

P. Walters: An Introduction to Ergodic Theory, Springer, 1982.

K. Petersen: Ergodic Theory, Cambridge Univ. Press, 1983

Last update: T_KPMS (16.05.2013)
Teaching methods -

Lecture.

Last update: T_KPMS (16.05.2013)
Requirements to the exam -

Oral exam according to sylabus.

Last update: Zichová Jitka, RNDr., Dr. (13.05.2023)
Syllabus -

1. Endomorphisms and automorphisms of probability spaces.

2. The Poincaré recurrence theorem.

3. The Birkhoff ergodic theorem and its consequences.

4. Examples.

5. Entropy and isomorphism of dynamical systems.

Last update: T_KPMS (16.05.2013)
Entry requirements -

Students should be acquianted with reasonably advanced mathematical analysis, in particular with measure theory and very basic notions of functional analysis.

Last update: Seidler Jan, RNDr., CSc. (28.05.2019)