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401-5371-00L 8 Credits
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Differential Equations and Dynamical Systems

Gewöhnliche Differentialgleichungen und dynamische Systeme

VVZ CR n/a

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
  • Mon 13:15-15:00 (HG E 1.1)
  • Tue 15:15-17:00 (HG E 3)
4 h weekly

Offered In