Zeitraum: 14.06.2018 16:00 Uhr - 18:00 Uhr
Ort: Carl-Zeiß-Straße 3, SR 308
Donnerstag, 14. Juni 2018, 16:30 Uhr, Carl-Zeiß-Str. 3, SR 308
Prof. Dr. Michael Dellnitz (Universität Paderborn)
Thema: Glimpse of the Infinite – on the Approximation of the Dynamical Behavior for Delay and Partial Differential Equations
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 finitedimensional space. 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.