Lecture: Chaos in higher-dimensional systems
- Wintersemester 2019/2020
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
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.
To discuss questions on the lectures and exercise sheets
and to exchange ideas a mailing list has been set up.
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Information on Python
German introduction to python/numpy/matplotlib
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
Point your web-browser to the given link
To create a new notebook, use File/New/Notebook
using Python 3
For an example see
which will look as
Exercises, references, code, ...
All this can be found here
(password protected, see first lecture).
Last modified: 07 November 2019, 15:54:07, Arnd Bäcker
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