!DOCTYPE html> JV: Nonlinear Dynamics and Pattern Formation

# SoSe2021. Pattern Formation and Nonlinear Dynamics

## News

 2021 04 29 Problem set 3 is available as PDF file and in the wiki, where we have discussion pages for the exercises. 2021 04 22 Problem set 2 is available as PDF file and in the wiki, where we have discussion pages for the exercises. 2021 04 15 We agreed about the times for the seminars and the lectures as indicated below. I updated problem 3 of problem set 1 to account for the fact that the centrifugal governor was not treated in class. More details are given in the wiki, where I also provide discussion pages for the exercises. Please contact me if you have are no account for the wiki. 2021 04 09 We will have our first lectures on 13 April 2021 at 15:00 in BBB (no access code required).

### Topics

 Dynamical Systems. characterization of flows, critical points, stability bifurcations, normal forms, center manifolds chaos, routes to chaos, symbolic dynamics Fractals. fractal dimensions, multifractals, thermodynamic formalism diffusion limited aggregation, snow flakes, breath figures Pattern Formation. linear and non-linear stability multiscale analysis, amplitude equations, Eckhaus and Benjamin-Feir instabilities hydrodynamic systems, nonlinear waves, turbulence reaction-diffusion systems, Turing instabilities

### Background and Supporting Material for Lectures

I will use Python and Sage for numerical studies and visualization. The script files are notebooks that run interactively in Jupyter. Please store them on your computer, start Jupyter, and then open the notebook. The files contain absolutely minimalistic explanations and comments. I assume that you know what they are intended to do because we discussed the problems in class.

As introductions to Python and Sage I recommend the books Steward: "Python for Scientists" and Zimmermann u.a.: "Computational Mathematics with SageMath".

 13 April 2021 Pojman movie page» and Strogatz movie»

### Problem Sets

 Set Date Topic PDF Hints 01. 2021 04 09 Qualitative Analysis (PDF file, 220kB) » ad 1.1d: How Grasshoppers Jump » 02. 2021 04 22 Basics in Dynamical Systems (PDF file, 95kB) » 03. 2021 04 29 1D Maps (PDF file, 90kB) »

### Meetings

 Course. Tue 13 – 15 Wed 12 – 14 Exercise Sessions. Mon 15 – 17

### Exams

There will be oral exams immediately after the end of the term.

### Literature

 G. Nicolis Introduction to Nonlinear Science Cambridge UP, 1995. H. Haken Synergetics. An Introduction Springer, 1983. E. Ott Chaos in Dynamical Systems Cambridge UP, 1993. M. Cross, H. Greenside Pattern Formation and Dynamics in Nonequilibrium Systems Cambridge UP, 2009.

 U. Behn Literature List (PDF) Links of Interest P. Cvitanovic, et al The Chaos Book Scholarpedia Dynamical Systems