Lecture: Chaos in higher-dimensional systems - Wintersemester 2022/2023

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.

Monday 3. DS (11:10-12:40)
Thursday 3. DS (11:10-12:40)


The lecture starts on Monday, 10th October 2022.

To subscribe: OPAL and also join the Matrix room (link in OPAL).
(Note that OPAL is typically down on the first day of the winter term...)

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

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.

Current plan for the lecture (05.08.2022, Update 28.09.2022)

Unfortunately, high numbers of COVID-19 cases are likely at the beginning of the term, as different epidemiological models suggest.
Therefore at least the lectures in the first week will be done online so that there will no changes on short notice.
Depending on the actual situation we will then either continue online, or switch to on-site lectures and tutorial sessions. An update on this will be given beginning of October.
Update (28.09.2022): In view of the surge in cases, the course will be done online throughout the whole term.
If you have any questions before, don't hesitate to contact me by E-mail!

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 discussed together. 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 OPAL.
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: 28 September 2022, 10:16:40, Arnd Bäcker
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