Email H. Bruin for further information for this course.
Day | Time | Room | from | to |
---|---|---|---|---|
Tuesday | 15:00-16:30 | HS13 | 2.3.2021 | 29.06.2021 |
Friday | 9:45-10:30 | HS13 | 5.3.2021 | 25.06.2021 |
Friday (Proseminar) | 10:30-11:15 | HS13 | 5.3.2021 | 25.06.2021 |
Basic notions for continuous and discrete dynamical systems; flows, attractors, and chaos; stability of stationary points by linearization and by Lyapunov functions, Poincaré-Bendixson theory, bifurcations.
Day | Material | |
---|---|---|
Week 1 | ||
2/3/2021 | Introduction, 1-D ODE Stationary points and their stability simple polulation growth models |
Notes of lecture 1 Lecture on a population dynamics model by Nagar. |
5/3/2021 | Quadratic family Cobweb diagram Feigenbaum diagram | Notes of lecture 2 (with typos corrected).
The link of recording is sent to you in the email of March 5. 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 constant are not part of the course material.) |
Week 2 | ||
9/3/2021 | Bifurcations in 1D (transcritical, saddlenode/fold, pitchfork) | |
12/3/2021 | No class (Rektorstag) | |
Week 3 | ||
16/3/2021 | Sensitive dependence on initial conditions Mathematical chaos (in the sense of Devaney) Lyapunov exponents |
Notes of lecture 3
Lecture on sensitive dependence on initial conditions by Nagar. Lecture on Devaney chaos by Nagar. |
19/3/2021 | Proseminar | Exercises 1-5 |
Week 4 | ||
23/3/2021 | Linear systems Structural stability Hartman-Grobman Theorem |
Lecture by Strogatz Exercise + solution on Structural stability |
27/3/2021 | Lotka-Volterra Predator-Prey model Lyapunov functions |
Lecture by Strogatz |
Week 5 | This is after the Easter break | |
13/4/2021 |
Limit cykels Van der Pol equation Hopf bifurcation |
Lecture by Strogatz |
16/4/2021 | Proseminar | Exercises 6-10 |
Week 6 | ||
20/4/2021 | Symbolic dynamics and Markov partitions
Sharkovskii's Theorem |
Notes of the lecture on symbolic dynamics Nagar's Lecture 23 on introduction to symbolic dynamics. Nagar's Lecture 17 on transitivity and Devaney chaos and Sharkovskiy's Theorem. Some typed notes on Symbolic dynamics |
23/4/2021 | Smale's Horseshoe |
Notes of the lecture on Smale's horse-shoe Nagar's Lecture 12 on dynamics of the horseshoe attractor. |
Week 7 | ||
27/4/2021 | Poincaré-Bendixson Theorem |
Notes of the Poincaré-Bendixson Theorem Lecture by Strogatz |
30/4/2021 | Proseminar | Exercises 11-13 |
Week 8 | ||
4/5/2021 | Circle homeomorphisms rotation numbers |
Notes of the lecture on circle homeomorphisms |
7/5/2021 | canceled | |
Week 9 | ||
11/5/2021 | The cusp bifurcation hysteresis |
Notes of the cusp bifurcation
Recorded lecture on the cusp bfurcation will be posted here. Lecture by Strogatz |
14/5/2021 | canceled | |
Week 10 | ||
18/5/2021 | | |
21/5/2021 | Proseminar: Exercises 13-16. | |
Week 11 | ||
25/5/2021 | No class Vorlesungsfrei | |
28/5/2021 | Oscillators |
Notes of the lecture on oscillators
Lecture by Wyslouch |
Week 12 | ||
1/6/2021 | Hamiltonian dynamics Euler-Lagrange equations |
Notes of the lecture on Hamiltonian dynamics
Online lecture by Strogatz |
4/6/2021 | Proseminar | Exercises 15-18. |
Week 13 | ||
8/6/2021 | Noether's Theorem n-body problem. |
Notes of the lecture on Noether's Theorem
Further text on Hamiltonian dynamics and the n-body problem |
11/6/2021 | Kepler's Problem 2-body problem | |
Week 14 | ||
15/6/2021 | Lorenz attractors |
Lectures by Strogatz on the Lorenz system and
another one.
Notes of the lecture on the Lorenz system |
18/6/2021 | Proseminar | Exercises 19-22 |
The course will be given in English
Contents of the course (B = Exercises , S = Schmeiser's notes, T = Teschl's book), St = Strogatz lecture on youtube.
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 |