10.1007/978-3-030-51264-4_3
Gerlach, Raphael
Raphael
Gerlach
Ziessler, Adrian
Adrian
Ziessler
The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems
Springer
2020
2020-08-14T15:02:22Z
2020-08-14T15:23:36Z
book_chapter
https://ris.uni-paderborn.de/record/17994
https://ris.uni-paderborn.de/record/17994.json
9783030512637
2198-4182
In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.