Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Applied Analysis and Computational Mathematics
- Code
- dindif1u0um17gm
- Title
- Dynamical systems and differential equations 1 (p)
- Usual semester
- Spring
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the modern notions of dynamical systems Ability: to understand and use the modern tools of dynamical systems Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. Autonomy and Responsibility: based on the gained knowledge in modern dynamical systems methods, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Topological equivalence, classification of linear and nonlinear systems. Stable, unstable, centre manifolds theorems, Hartman - Grobman theorem. Periodic solutions and their stability. Bifurcations in dynamical systems, basic examples. Definitions of local and global bifurcations. Saddle-node bifurcation, Andronov-Hopf bifurcation. Discrete dynamical systems. Classification according to topological equivalence. 1D maps, the tent map and the logistic map. Symbolic dynamics.
- Assessment method
- term grade
- Bibliography
- lecture notes