book chapter published Raphael Gerlach author 32655 Adrian Ziessler author OliverJunge editor OliverSchütze editor SinaOber-Blöbaum editor KathrinPadberg-Gehle editor 101 department 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. Springer International Publishing2020 eng 2198-4182 2198-4190 9783030512637 978303051264410.1007/978-3-030-51264-4_3 30466-85 Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:<a href="https://doi.org/10.1007/978-3-030-51264-4_3">10.1007/978-3-030-51264-4_3</a> Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control. Cham: Springer International Publishing, 2020. <a href="https://doi.org/10.1007/978-3-030-51264-4_3">https://doi.org/10.1007/978-3-030-51264-4_3</a>. R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in <i>Advances in Dynamics, Optimization and Computation</i>, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85. Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:<a href="https://doi.org/10.1007/978-3-030-51264-4_3">10.1007/978-3-030-51264-4_3</a>. R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 66–85. @inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems, Decision and Control}, title={The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}, volume={304}, DOI={<a href="https://doi.org/10.1007/978-3-030-51264-4_3">10.1007/978-3-030-51264-4_3</a>}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control} } Gerlach, R., &#38; Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (Vol. 304, pp. 66–85). Springer International Publishing. <a href="https://doi.org/10.1007/978-3-030-51264-4_3">https://doi.org/10.1007/978-3-030-51264-4_3</a> 179942020-08-14T15:02:22Z2023-11-17T13:13:25Z