TY - CHAP
AB - 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.
AU - Gerlach, Raphael
AU - Ziessler, Adrian
ED - Junge, Oliver
ED - Schütze, Oliver
ED - Ober-Blöbaum, Sina
ED - Padberg-Gehle, Kathrin
ID - 17994
SN - 2198-4182
T2 - Advances in Dynamics, Optimization and Computation
TI - The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems
VL - 304
ER -