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Nonlinear Dynamics & Pattern Formation
Wiki with Exercises, Notes, Hints, and a Feedback-Forum
Jürgen Vollmer, Uni Leipzig, SoSe2021
Classes
| Time | Room | Access Code |
|---|---|---|
| Tue, 13–15 | BigBlueBotton Channel | $\quad$ 439827 |
| Wed, 12–14 | BigBlueBotton Channel | $\quad$ 439827 |
Notes of Online Lectures are available here
Online seminars
| Time | Room | Access Code |
|---|---|---|
| Mo, 15 –17 | BigBlueBotton Channel | $\quad$ 439827 |
Notes of Seminars are available here
Recommended Literature
- Gregoire Nicolis. Introduction to Nonlinear Science (Cambridge UP, 1995)
- Ed Ott. Chaos in Dynamical Systems (Cambridge UP, 1993)
- Michael Cross, Henry Greenside. Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge UP, 2009)
Exercise Sheets
Each week there will be a set of problems. For each problem there will be a discussion page, and eventually we will discuss the solutions in the seminar. On request I also offer suggestions for further study.
| Set | Date | Topic | |
|---|---|---|---|
| 1 | 2021 04 13 | Qualitative Analysis | 220 kB |
| 2 | 2021 04 20 | Basics in Dynamical Systems | 82 kB |
| 3 | 2021 04 27 | 1D maps | 90 kB |
| 4 | 2021 05 04 | Fractals and Symbolic Dynamics | 106 kB |
| 5 | 2021 05 11 | 1D measures | 85 kB |
| 6 | 2021 05 18 | From 1D to 2D maps | 79 kB |
| 7 | 2021 05 25 | 2D maps and their stable/unstable manifolds | 125 kB |
| 8 | 2021 06 02 | From maps to flows |
Sage Notebooks
For selected problems I will set up a Sage playground, where you can explore the solutions to a range of problems in theoretical mechanics based on interactive Sage templates.
Participation
- extension of the wiki and requests for help
- tips and tricks concerning issues with university emails, moodle, almaweb, this wiki, etc
- general discussion, feedback, and information about you
Three are discussion forms on these pages. Viable suggestions and solutions will be promoted from the discussion to Howtos in the main part of the pages. Regular contributors will earn the right to directly edit the pages.
Seminar Talks
- Frederik.
- Konstantin. Turing mechanism and the Schnakenberg system (maybe also chemical pattern formation?)
- Lenoard. Bifurcation analysis for the Swift-Hohenberg-eq (1D).
- + possibly extended version: https://rveltz.github.io/BifurcationKit.jl/dev/tutorials2b/#The-Swift-Hohenberg-equation-on-the-GPU-(non-local)-1
- please also check out
- Robert. caustics