Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Analysis
- Code
- disdin1u0um17em
- Title
- Discrete dinamical systems (l)
- Usual semester
- Spring
- Published semester
- 2025/26/2
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the modern notions and methods of Discrete Dynamical Systems Abilityto understand and use the modern Discrete Dynamical Systems Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. The aim to apply the mathematical knowledge for a wide range of problems Autonomy and Responsibility: based on the gained knowledge in modern Discrete Dynamical Systems, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Topological transitivity and minimality. Omega limit sets. Symbolic Dynamics. Topological Bernoulli shift. Maps of the circle. The existence of the rotation number. Invariant measures. Krylov-Bogolubov theorem. Invariant measures and minimal homeomorphisms. Rotations of compact Abelian groups. Uniquely ergodic transformations and minimality. Unimodal maps. Kneading sequence. Eventually periodic symbolic itinerary implies convergence to periodic points. Ordering of the symbolic itineraries. Characterization of the set of the itineraries. Equivalent definitions of the topological entropy. Zig-zag number of interval maps. Markov graphs. Sharkovskii’s theorem. Foundations of the Ergodic theory. Maximal and Birkhoff ergodic theorem.
- Assessment method
- exam
- Bibliography
- lecture notes