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Course, academic year 2018/2019
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Chapters from discrete dynamical systems - NMMA479
Title in English: Kapitoly z diskrétních dynamických systémů
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016 to 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jozef Bobok, CSc.
Mgr. Benjamin Vejnar, Ph.D.
Class: DS, geom. a topologie, gl. analýza a ob. struktury
M Mgr. MA
M Mgr. MA > Volitelné
Obecná topologie a teorie kategorií
Classification: Mathematics > Differential Equations, Potential Theory, Topology and Category
Annotation -
Last update: T_KMA (27.04.2016)
The lecture will offer a self-contained introductory exposition of the theory of low-dimensional discrete dynamical systems. Several principal theoretical concepts and methods for the study of asymptotic properties of an individual trajectory and also the global complexity of the orbit structure will be introduced. A number of fundamental examples will be discussed.
Course completion requirements - Czech
Last update: Mgr. Benjamin Vejnar, Ph.D. (10.06.2019)

Předmět je zakončen zkouškou.

Literature -
Last update: T_KMA (27.04.2016)

1. A. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge University Press, Cambridge, 1995.

2. P. Kitchens, Symbolic dynamics: one-sided, two-sided, and countable state Markov shifts, Universitext, Springer-Verlag, Berlin Heidelberg New York, 1998.

3. P. Walters, An introduction to ergodic theory, Springer-Verlag, Berlin Heidelberg New York, 1982.

Requirements to the exam - Czech
Last update: Mgr. Benjamin Vejnar, Ph.D. (06.10.2017)

Zkouška má ústní formu s písemnou přípravou. Studentovi bude zadáno téma, ke kterému si připraví související věty, definice a důkazy.

Syllabus -
Last update: T_KMA (27.04.2016)

Our lecture will be focused on both topological and measure-theoretical dynamical systems. The main attention will be paid to important dynamical phenomena and related results: periodicity, recurrence, minimality and transitivity, complexity measured by topological entropy, invariant measure, measure-theoretical entropy and variational principle, ergodicity and mixing. All parts will be illustrated by examples.

 
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