{"type":"journal_article","publication_status":"published","volume":18,"date_updated":"2023-11-17T13:13:09Z","publication":"SIAM Journal on Applied Dynamical Systems","department":[{"_id":"101"}],"title":"The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques","page":"1265-1292","intvolume":" 18","user_id":"32655","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"}],"date_created":"2020-04-16T14:04:20Z","status":"public","citation":{"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.","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} }","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.","short":"A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems 18 (2019) 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.","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"},"issue":"3","author":[{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Gerlach, Raphael","last_name":"Gerlach","first_name":"Raphael","id":"32655"}],"year":"2019","publication_identifier":{"issn":["1536-0040"]},"main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/18M1204395"}],"doi":"10.1137/18m1204395","language":[{"iso":"eng"}],"_id":"16708"}