Lecture: Chaos in higher-dimensional systems - Wintersemester 2025/2026

Time/place

3-Body motion Format: 3+1, i.e. one week with two lectures, and the following with one lecture and one tutorial session.

Audience: Bachelor und Master (Modul Physikalische Vertiefung), Doktoranden, IMPRS

Tuesday 3. DS (11:10-12:40), BZW/A120
Thursday 5. DS (14:50-16:20), BZW/A120
The lecture starts on Tuesday, 14th October 2025.

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Contents

Many physical systems of interest have more than two degrees of freedom which can lead to highly complicated dynamical behavior. Examples are the solar system, atoms and molecules, particle accelerators, or chains of coupled oscillators. In this course we give a general introduction to the dynamics of such higher--dimensional systems. Central for the understanding are invariant objects like fixed points, periodic trajectories, invariant tori, and stable and unstable manifolds. So-called non-linear resonances play a crucial role as they are at the heart of the famous Arnold diffusion, which exclusively occurs in higher-dimensional systems.
The course will make use of a combination of rigorous mathematical results (including ideas of their proofs), physicists reasoning (aka hand-waving of different severity) and numerical investigations.

Last modified: 08 September 2025, 10:15:00, Arnd Bäcker
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