Email H. Bruin for further information for this course.
Day | Time | Room | from | to |
---|---|---|---|---|
Tuesday | 16:45-18:15 | SR8 Kolingasse | 2.3.2024 | 27.06.2021 |
Friday Lecture (odd weeks) | 11:30-13:00 | SR7 | 19.3.2024 | 30.06.2021 |
Friday Proseminar (even weeks) | 11:30-13:00 | SR7 | 19.3.2024 | 30.06.2021 |
Day | Topic | Material |
---|---|---|
Week 1 | ||
1/3/2024 | Introduction, 1-D ODE Stationary points and their stability simple polulation growth models |
Notes of lecture 1 Lecture on a population dynamics model by Anima Nagar |
Week 2 | ||
5/3/2024 | Quadratic family Cobweb diagram Feigenbaum diagram | Notes of lecture 2.
Applets used in the lecture: cobweb diagram, the bifurcation diagram and another one , all for the logistic family. Lecture by Strogatz A video on the Feigenbaum diagram. (Feigenbaum's constant is not part of the course material.) |
8/3/2024 | Proseminar | Exercise 1-5 of the Exercise sheet. The checkmark list on Moodle. |
Week 3 | ||
12/3/2024 | Rektorstag -- no class | |
15/3/2024 | Class canceled | |
Week 4 | ||
19/3/2024 | Bifurcations in 1D | |
22/3/2024 | Proseminar | Exercise 6,7,8,9 and 11 of the Exercise sheet. The checkmark list on Moodle. |
Week 5 | ||
9/4/2024 | Mathematical Chaos Topological transitivity | Notes of today's lecture |
12/4/2024 | Schwarzian Derivative | Notes of today's lecture |
Week 6 | ||
16/4/2024 | Hartman-Grobman | Notes of today's lecture Online lecture by Strogatz |
19/4/2024 | Proseminar |
Exercise 11, 16, 17 and 18 of the Exercise sheet
and also prove the following properties of the Schwarzian derivative (see also the lecture notes of April 12): 1. S(f o g) = (Sf) o g . (g')2 - Sg. 2. Sf = 0 if and only if f is a Möbius transformation. Hint: Show that Sf = -2√(f') . (1/√(f'))''. Then Sf = 0 is equivalent to (1/√(f'))'' = 0, and that is easier to solve. The checkmark list on Moodle. |
Week 7 | ||
23/4/2024 | Lotka-Volterra (predator-prey) systems Lyapunov functions. |
Notes of today's lecture Lecture by Strogatz. |
26/4/2024 | Limit Cycles Van der Pol system ω-limit and α-limit sets | |
Week 8 | ||
30/4/2024 | ω-limit and α-limit sets
Poincaré-Bendixson Theorem | |
19/4/2024 | Proseminar |
Exercise 17 and 18 of the Exercise sheet
and also prove the following properties of the Schwarzian derivative (see also the lecture notes of April 12): 1. S(f o g) = (Sf) o g . (g')2 - Sg. 2. Sf = 0 if and only if f is a Möbius transformation. Hint: Show that Sf = -2√(f') . (1/√(f'))''. Then Sf = 0 is equivalent to (1/√(f'))'' = 0, and that is easier to solve. The checkmark list on Moodle. |
Assessment of the course will be by oral exam, as discussed in class.
The default language is English, but German is possible too.
Smale's horseshoe | A homoclinic tangle | Another homoclinic tangle |