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Differential Equations and Dynamical Systems
Gewöhnliche Differentialgleichungen und dynamische Systeme
Last Updated: 2026-02-05 14:59:47
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
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Gewöhnliche Differentialgleichungen und dynamische Systeme |
|
4 h weekly |
Offered In
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Ausbildung für den Didaktischen Ausweis (Mathematik bzw. Physik) (Studierende im Bachelorstudiengang Mathematik, die die Ausbildung für das Höhere Lehramt in Mathematik im WSA 05/06 beginnen wollen, studieren gemäss den Bestimmungen für den Didaktischen Ausweis. Das entsprechende Reglement ist im Reglement für den Diplomstudiengang Mathematik enthalten. Mit der Ausbildung für das Höhere Lehramt kann beginnen, wer im Bachelorstudium mindestens 110 Kreditpunkte erworben hat.)
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