Lecture: Chaos in higher-dimensional systems - Wintersemester 2019/2020


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

Monday 5. DS (14:50-16:20), BZW/A120
Tuesday 5. DS (14:50-16:20), WIL/A221

The lecture starts on Monday, 14th October 2019.

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


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.

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Information on Python

German introduction to python/numpy/matplotlib [einfuehrung.pdf, einfuehrung2.pdf].
A detailed guide to python and numpy/scipy/matplotlib are the Python Scientific Lecture Notes.

Jupyter notebooks for symbolic computations

To locally start the notebook server run in a konsole
  jupyter lab
  jupyter notebook
Point your web-browser to the given link
To create a new notebook, use File/New/Notebook using Python 3. For an example see standard_map.ipynb, which will look as standard_map.html.

Exercises, references, code, ...

All this can be found here (password protected, see first lecture).
Last modified: 07 November 2019, 15:54:07, Arnd Bäcker
Computational Physics Group Home.