{"user_id":"32655","department":[{"_id":"101"}],"external_id":{"arxiv":["1902.08824"]},"_id":"16711","language":[{"iso":"eng"}],"ddc":["510"],"type":"preprint","publication":"arXiv:1902.08824","status":"public","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."}],"author":[{"full_name":"Gerlach, Raphael","id":"32655","last_name":"Gerlach","first_name":"Raphael"},{"first_name":"Péter","full_name":"Koltai, Péter","last_name":"Koltai"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"date_created":"2020-04-16T14:06:21Z","oa":"1","date_updated":"2024-09-24T12:09:27Z","main_file_link":[{"url":"https://arxiv.org/abs/1902.08824","open_access":"1"}],"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems","has_accepted_license":"1","citation":{"ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. <i>arXiv:190208824</i>. Published online 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems,” <i>arXiv:1902.08824</i>. 2019.","chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","apa":"Gerlach, R., Koltai, P., &#38; Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. In <i>arXiv:1902.08824</i>.","short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).","mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 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} }"},"year":"2019"}