Kolloquien und Oberseminare Übersicht Detail

Speaker:
Prof. Dr. Michael Dellnitz (Universität Paderborn)

This event is part of an event series „Schwerpunktkolloquium Analysis und Numerik“.

Abstract: Over the last years so-called set oriented numerical methods have been developed for the analysis of the long-term behavior of finite-dimensional dynamical systems. The underlying idea is to approximate the corresponding objects of interest – for instance global attractors or related invariant measures – by box coverings which are created via multilevel subdivision techniques. That is, these techniques rely on partitions of the (finite-dimensional) state space, and it is not obvious how to extend them to the situation where the underlying dynamical system is infinite-dimensional. In this talk we will present a novel numerical framework for the computation of finitedimensional dynamical objects for infinite-dimensional dynamical systems. Within this framework we will extend the classical set oriented numerical schemes mentioned above to the infinite-dimensional context. The underlying idea is to utilize appropriate embedding techniques for the reconstruction of global attractors in a certain finitedimensionalspace. We will also illustrate our approach by the computation of global attractors both for delay and for partial differential equations; e. g. the Mackey-Glass equation or the Kuramoto-Sivashinsky equation.