Colloquium: Christian Pötzsche (Alpen-Adria Universität Klagenfurt, Austria)

When:
May 9, 2018 @ 3:30 pm – 4:30 pm
2018-05-09T15:30:00-10:00
2018-05-09T16:30:00-10:00
Where:
Keller 401

Title: Nonautonomous Dynamics

Christian Pötzsche
Alpen-Adria Universität Klagenfurt, Austria
christian.poetzsche@aau.at

http://wwwu.uni-klu.ac.at/cpoetzsc/Christian_Potzsche/english.html

The theory of dynamical systems has seen a remarkable progress over the last 100 years, beginning with the contributions of Poincaré and Lyapunov to a contemporary detailed understanding of the attractor for various infinite-dimensional systems. This success is partly due to the restriction to autonomous systems. However, many real-world problems are actually nonautonomous. That is, they involve time-dependent parameters, controls, modulation and various other effects. Special cases include periodically or almost periodically forced systems, but in principle the time dependence can be arbitrary. As a consequence, many of the now well-established concepts, methods and results for autonomous systems are no longer applicable and require appropriate extensions.

We discuss several basic ingredients from the theory of nonautonomous dynamical systems. Among them are (pullback) convergence, the dichotomy spectrum (to indicate stability) and approaches to understand nonautonomous bifurcations.