Dynamical Systems

Winter 2002/03

Prof. Dr. Volker Enß (Enss), Dr. Olaf Post

Deutsche Version, English version
( Listing in the online course list Campus of the RWTH)

Dates: Place: Start:
Lecture 4 hours Mo 14:00 - 15:30 Room 224 (Main Bldg.) Oct. 21, 2002
Wed 8:15 - 9:45 Room 224
Exercises 2 hours Mo 15:45 - 17:15 Room 224 Oct. 28, 2002

Problems for Exercises, Maple worksheets

Contents:
We study systems with a time-evolution. This can be continuous (systems of ordinary differential equations in n-dimensional space) or discrete (iterated maps). We begin with discrete dynamical systems.

The theory of dynamical systems analyses the long time behavior (equilibria, periodic points, stability, chaos, ...). We study structural stability of the system under perturbations as well as bifurcations (qualitative changes of behavior) when parameters are varied.

Some more keywords:
Symbolic dynamics, Bernoulli-shift, hyperbolic invariant set, attractor, homoclinic point, and - if time permits - shadowing lemma, Melnikov's theorem.

Numerical simulations will be used to visualize the phenomena.

For Students of Mathematics, Physics, ... , 5th semester or higher

Prerequisits: Linear algebra, multidimensional analysis, basics of ODE.

Due to the wide range of possible topics the detailed selection of the material to be covered can be adjusted to the prerequisits and interests of the audience.

A selection of textbooks and monographs, further comments will be given in the lecture:

D. K. Arrowsmith, C. M. Place: An introduction to Dynamical Systems, Cambridge U. Press, 1994
A. Katok, B. Hasselblatt: Introduction to the Modern Theory of Dynamical Systems, Cambridge U. Press, 1995, 1997
R.L. Devaney: An Introd. to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley 1989
K.T. Alligood, T.D. Sauer, J.A. Yorke: Chaos; An Introduction to Dynamical Systems, Springer 1997
M.C. Irvin: Smooth Dynamical Systems, Academic Press 1980
J. Guckenheimer, P. Holmes: Nonlinear Oszillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer 1983
J. Hale, H. Kocak: Dynamics and Bifurcations, Springer 1991
L. Perko: Differential Equations and Dynamical Systems, Springer 1991, 1996
S. Wiggins: Introd. to Applied Nonlinear Dynamical Systems and Chaos,Springer 1990

Related: A seminar in this semester about related topics in ODE.


disclaimer, Oct. 2002, Volker Enß