MICHAEL DELLNITZ
Department of Mathematics and Computer Science
University of Paderborn
D-33095 Paderborn, Germany
http://math-www.uni-paderborn.de/~agdellnitz/
dellnitz@uni-paderborn.de
Abstract:
Over the past few years so-called set-oriented numerical
methods have been developed for the numerical study
of dynamical systems. These methods do not just allow to
compute directly -- i.e., by avoiding long term
simulations of the underlying system -- chain recurrent
sets or invariant manifolds but they can also be used to
approximate statistical quantities such as natural
invariant measures. In this talk an overview about
recent accomplishments in this area will be given. In
particular, two concrete applications of these techniques
will be presented: the approximation of so-called almost
invariant sets and the construction of reliable
global zero finding procedures.