{"page":"1265-1292","doi":"10.1137/18m1204395","issue":"3","publication_status":"published","date_created":"2020-04-16T14:04:20Z","abstract":[{"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","lang":"eng"}],"publication":"SIAM Journal on Applied Dynamical Systems","date_updated":"2023-11-17T13:13:09Z","type":"journal_article","main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/18M1204395"}],"language":[{"iso":"eng"}],"citation":{"chicago":"Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i> 18, no. 3 (2019): 1265–92. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>.","apa":"Ziessler, A., Dellnitz, M., &#38; Gerlach, R. (2019). The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>, <i>18</i>(3), 1265–1292. <a href=\"https://doi.org/10.1137/18m1204395\">https://doi.org/10.1137/18m1204395</a>","short":"A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems 18 (2019) 1265–1292.","ieee":"A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, pp. 1265–1292, 2019, doi: <a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","bibtex":"@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}, volume={18}, DOI={<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>}, number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292} }","mla":"Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 18, no. 3, 2019, pp. 1265–92, doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>.","ama":"Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques. <i>SIAM Journal on Applied Dynamical Systems</i>. 2019;18(3):1265-1292. doi:<a href=\"https://doi.org/10.1137/18m1204395\">10.1137/18m1204395</a>"},"user_id":"32655","volume":18,"publication_identifier":{"issn":["1536-0040"]},"department":[{"_id":"101"}],"title":"The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques","_id":"16708","author":[{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"32655","last_name":"Gerlach","full_name":"Gerlach, Raphael","first_name":"Raphael"}],"year":"2019","intvolume":"        18","status":"public"}