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Ordinary Differential Equations and Dynamical Systems
Gewöhnliche Differentialgleichungen und dynamische Systeme
Last Updated: 2026-02-05 15:18:41
Abstract
Equilibria and their Stability, introduction to KAM-Theory, Chaotic Behaviour: Shadowing Techniques
Objective
Students will be familiar with basic notions, techniques and results of the geometric theory of ordinary differential equations and dynamical systems. The course is supplemented with plenty of excercises so that students can deepen their understanding and get accustomed to apply the theory. At as many places as possible relationships to school mathematics will be emphasized, in particular some of the excercises will be devoted to this type of transfer.
Content
Liapunov stability (linear systems, lnearization, Liapunov functions), hyperbolic points and their geometry (stable und unstable manifolds), introduction to Kolmogorov-Arnold-Moser theory (functional-theoretic center problem, small divisors and number theoretical considerations, Newton-Rüssmann type iteration schemes), Moser`s Twist Theorem, applications), chaotic behavior in simple systems (hyperbolic sets, shadowing, Smale horseshoe, applications).
Resources
Lecture Notes
A number of handouts will be provided.
Literature
A list of references will be distributed in the course.
General Information
- Language
- German
- Levels
- DZ , BSC , SHE , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Gewöhnliche Differentialgleichungen und dynamische Systeme |
|
2 h weekly |
| colloquium | Gewöhnliche Differentialgleichungen und dynamische Systeme |
|
1 h weekly |
Offered In
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Mathematics TC (Detailed information on the programme at: )
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Mathematics MAS SHE (Detailed information on the programme at: )
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Spec. Courses in Respective Subject with Educ. Focus (Major Subject) (MAS SHE in 2 Subjects in One-Step Procedure: no courses from this category have to be completed.)
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