Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Analysis
- Code
- dinrsz1u0um17em
- Title
- Dynamical systems (l)
- Usual semester
- Autumn
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: The purpose of the course to introduce basic concepts and examples of Dynamical Systems. Ability: to understand and use methods related to 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 Dynamical Systems, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Contractions, fixed point theorems. Examples of Dynamical Systems: Newton's method, interval maps, the quadratic family, differential equations, rotations of the circle. Graphical analysis. Hyperbolic fixed points. Cantor sets as hyperbolic repelling sets. Sequence spaces as metric spaces. Symbolic dynamics and coding. Topological transitivity, sensitive dependence on initial conditions, chaos/chaotic maps, structural stability, period three implies chaos. The Schwarzian derivative. Bifurcation theory. Period doubling. Linear maps and linear differential equations in the plane. Translations and linear flows on the torus. Conservative systems.
- Assessment method
- exam
- Bibliography
- lecture notes