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
- 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 (Recommended:) B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995. Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition. Addison WesleyStudies in Nonlinearity. Addison WesleyPublishing Company, Advanced Book Program, Redwood City, CA, 1989.
- Recommended bibliography
- B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995. Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition. Addison WesleyStudies in Nonlinearity. Addison WesleyPublishing Company, Advanced Book Program, Redwood City, CA, 1989.