240115 Optimization and Dynamics (V) (SoSe 2013)

Course Objective:
The course gives an introduction to dynamical systems (discrete and continuous). Students shall learn the basic quantitative and qualitative methods to solve dynamical sytems and shall become acqainted with the typical phenomena arising in linear and non-linear systems.

Content:
will be adapted according to the knowledge and needs of the students, some items may be added or skipped.
dynamical systems with discrete time:
one--dimensional systems and n-dimensional systems
linear and non--linear systems
stability
bifurcations
period doubling
dynamical systems with continuous time:
linear differential equations
non-linear autonomous differential equations
existence and uniqueness of solutions
stability
flow
symbolic dynamics

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

first courses in linear algebra and analysis

Literaturangaben

R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989
D. K. Arrowsmith, An introduction to dynamical systems, Cambridge Univ. Press , 1994