## Numerics of Dynamical Systems (MA3333)

Prof. Dr. Oliver Junge### Content

Dynamical Systems are mathematical models of systems which change their state with time. Typical examples are (certain) ordinary or partial differential equations. A basic question for a such system is of course to compute its temporal evolution, given a particular initial condition, i.e. to*simulate*the system. Often, however, one is interested in the targeted computation of particular solutions, e.g. equilibrium points (i.e. states which do not change with time), periodic solutions or connecting orbits. In addition, many models from applications exhibit

*complicated dynamics*. Here, the question is how one can describe the dynamics of such systems over long time spans and how these descriptions can be reliably approximated numerically. These are questions which are being treated in this lecture, tying in with MA 3082

*Nonlinear Dynamics*.

### News

### Lecture/Tutorials

- Lecture: Tuesday, 12-14, MI 02.08.011
- Tutorials: Mondays, 16-18, MI 02.10.011, dates: 20.11., 11.12., 18.12., 8.1., 22.1., 5.2.
- Lecture notes, assignments, codes

### Exam

- date: Feb 19, 2018, 10:00 am
- room: MI 02.08.011
- duration: 60 minutes
- tools: you might bring one cheat sheet (A4, double sided)

### References

- Stuart, A.M.; Humphries, A.R.: Dynamical systems and numerical analysis, Cambridge University Press, 1998.
- Parker, T.S.; Chua, L.O.: Practical numerical algorithms for chaotic systems
^{}, Springer, New York, 1989. - Lasota, A.; Mackey, M.C.: Chaos, Fractals, and Noise
^{}, Springer, New York, 1994. - Dellnitz, M.; Froyland, G.; Junge, O.: The algorithms behind GAIO - Set oriented numerical methods for dynamical systems, B. Fiedler (ed.): Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, 2001.