SubjectsSubjects(version: 867)
Course, academic year 2019/2020
  
Ergodic Theory - NMTP532
Title: Ergodická teorie
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 4
Hours per week, examination: summer s.:3/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
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.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: T_KPMS (16.05.2013)
The lectures are devoted to basic properties of measureble dynamical systems, properties like recurrence, ergodicity and mixing being discussed in detail.
Aim of the course -
Last update: T_KPMS (16.05.2013)

Students will learn basic results about measurable dynamical systems.

Course completion requirements - Czech
Last update: RNDr. Jitka Zichová, Dr. (19.04.2018)

Složení ústní zkoušky.

Literature - Czech
Last update: T_KPMS (16.05.2013)

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

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

Teaching methods -
Last update: T_KPMS (16.05.2013)

Lecture.

Requirements to the exam - Czech
Last update: RNDr. Jan Seidler, CSc. (28.04.2020)

Zkouška je ústní, požadavky odpovídají sylabu předmětu v rozsahu, který byl presentován na přednáškách (včetně přednášek konaných

distanční formou).

Syllabus -
Last update: T_KPMS (16.05.2013)

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.

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

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

 
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