VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-5371-00L 4 Credits DZ , BSC , SHE , MSC D-MATH
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Ordinary Differential Equations and Dynamical Systems

Gewöhnliche Differentialgleichungen und dynamische Systeme

Lecturers & Examiners: Prof. em. Dr. Urs Kirchgraber
VVZ CR n/a

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
  • Tue 15:15-17:00 (HG F 5)
2 h weekly
colloquium Gewöhnliche Differentialgleichungen und dynamische Systeme
  • Wed 15:15-16:00 (HG F 5)
1 h weekly

Offered In