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Modul
Introduction to Dynamical Systems [M-MATH-106591]
Credits
6Recurrence
UnregelmäßigDuration
1 SemesterLanguage
German/EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-113263 | Introduction to Dynamical Systems | 6 |
Competence Certificate
The module will be completed with an oral exam of about 30 minutes.
Competence Goal
After successful completion of this module students
- can explain the significance of dynamical systems and give several examples;
- have acquired miscellaneous tools to prove the existence of special solutions and to analyze the local dynamics around them;
- master several techniques to describe global dynamics in certain classes of dynamical systems;
- identify various bifurcations and explain how these change the dynamics of the system;
- outline the main steps in establishing chaotic behavior.
Prerequisites
None
Content
- Flows
- Abstract dynamical systems
- Lyapunov functions
- Invariant sets
- Limit sets and attractors
- Hartman-Grobman theorem
- Local (un)stable manifold theorem
- Poincaré-Bendixson theorem
- Periodic orbits and Floquet theory
- Exponential dichotomies
- Melnikov functions
- Lin's method
- Hamiltonian dynamics
- Liénard systems
- Bifurcations
- Chaotic dynamics
- (Introduction to) Fenichel theory
- Center manifolds
- Dynamical systems associated with semilinear evolution equations
Recommendation
The following modules are strongly recommended: Analysis 1-2 and Linear Algebra 1-2. The module Analysis 4 is recommended.
Workload
Total workload: 180 hours
Attendance: 60 h
- lectures, problem classes and examination
Self studies: 120 h
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research on the course content,
- preparation for the module examination