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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.
Last update: T_KMA (27.04.2016)
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Předmět je zakončen zkouškou. Last update: Vejnar Benjamin, doc. Mgr., Ph.D. (10.06.2019)
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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. Last update: T_KMA (27.04.2016)
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Zkouška má ústní formu s písemnou přípravou. Studentovi bude zadáno téma, ke kterému si připraví související věty, definice a důkazy. Last update: Vejnar Benjamin, doc. Mgr., Ph.D. (06.10.2017)
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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. Last update: T_KMA (27.04.2016)
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