Lecture: Chaos in higher-dimensional systems
- Wintersemester 2021/2022
Format: 3+1, i.e. one week with two lectures,
and the following with one lecture and one tutorial session.
Monday 3. DS (11:10-12:40)
Tuesday 2. DS (09:20-10:50)
The lecture starts on Monday, 11th October 2021.
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.
Current plan for the lecture (10.08.2021, Update 30.09.2021)
Due to the increasing number of COVID-19 cases, the low vaccination
level in Saxony and the highly contagious delta variant
the lecture will not be held in physical presence.
Therefore we will make use of the flipped classroom concept
in which (most) material is handed out to you in form of notes before
we meet during the lecture hours in a video conference
(BigBlueButton will be used).
These meetings are intended as discussion rounds
in which you should ask as many questions as possible, which will be
Such questions may also be formulated upfront via different channels,
also allowing for anonymous questions (if you prefer).
The whole concept of a flipped classroom really works best, if
many questions are asked!
In addition, I will use the discussion rounds to
present numerical simulations and videos.
The first lecture will provide an overall introduction
without additional material handed out before.
To enroll to the course and recieve updates before the
start of the course and the link(s) to the
the video conferences, please add your name and E-mail via
Note: If you do not have a TU Dresden account, you have to register an account using your preferred E-mail address via Register
. As institution simply use TU Dresden
. After the registration process, return to OPAL course page
and click Enroll
If you have any questions, do not hesitate to contact me by E-mail!
Last modified: 30 September 2021, 08:26:15, Arnd Bäcker
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