Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

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)