--- _id: '16708' abstract: - lang: eng text: " In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for\r\nthe computation of such objects of finite dimensional systems with the results obtained in the work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis\r\nof partial differential equations and illustrate its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n" author: - first_name: Adrian full_name: Ziessler, Adrian last_name: Ziessler - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Raphael full_name: Gerlach, Raphael id: '32655' last_name: Gerlach citation: ama: Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. SIAM Journal on Applied Dynamical Systems. 2019;18(3):1265-1292. doi:10.1137/18m1204395 apa: Ziessler, A., Dellnitz, M., & Gerlach, R. (2019). The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. SIAM Journal on Applied Dynamical Systems, 18(3), 1265–1292. https://doi.org/10.1137/18m1204395 bibtex: '@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}, volume={18}, DOI={10.1137/18m1204395}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292} }' chicago: 'Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” SIAM Journal on Applied Dynamical Systems 18, no. 3 (2019): 1265–92. https://doi.org/10.1137/18m1204395.' ieee: 'A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,” SIAM Journal on Applied Dynamical Systems, vol. 18, no. 3, pp. 1265–1292, 2019, doi: 10.1137/18m1204395.' mla: Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” SIAM Journal on Applied Dynamical Systems, vol. 18, no. 3, 2019, pp. 1265–92, doi:10.1137/18m1204395. short: A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems 18 (2019) 1265–1292. date_created: 2020-04-16T14:04:20Z date_updated: 2023-11-17T13:13:09Z department: - _id: '101' doi: 10.1137/18m1204395 intvolume: ' 18' issue: '3' language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/epdf/10.1137/18M1204395 page: 1265-1292 publication: SIAM Journal on Applied Dynamical Systems publication_identifier: issn: - 1536-0040 publication_status: published status: public title: The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques type: journal_article user_id: '32655' volume: 18 year: '2019' ...