[{"abstract":[{"lang":"eng","text":"Embedding techniques allow the approximations of finite dimensional\r\nattractors and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and continuation methods. These approximations give a topological\r\none-to-one image of the original set. In order to additionally reveal their\r\ngeometry we use diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation, as well as for the attractor of the Mackey-Glass delay differential\r\nequation."}],"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems","_id":"16711","author":[{"first_name":"Raphael","last_name":"Gerlach","full_name":"Gerlach, Raphael","id":"32655"},{"last_name":"Koltai","first_name":"Péter","full_name":"Koltai, Péter"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"language":[{"iso":"eng"}],"date_updated":"2020-04-16T14:06:44Z","publication":"arXiv:1902.08824","citation":{"short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).","bibtex":"@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems}, journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}, year={2019} }","chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical Systems.” *ArXiv:1902.08824*, 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems,” *arXiv:1902.08824*. 2019.","apa":"Gerlach, R., Koltai, P., & Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. *ArXiv:1902.08824*.","mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical Systems.” *ArXiv:1902.08824*, 2019.","ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. *arXiv:190208824*. 2019."},"user_id":"47427","year":"2019","department":[{"_id":"101"}],"status":"public","type":"preprint","date_created":"2020-04-16T14:06:21Z"}]