preprint
Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems
Raphael
Gerlach
author 32655
Péter
Koltai
author
Michael
Dellnitz
author
101
department
Embedding techniques allow the approximations of finite dimensional
attractors and manifolds of infinite dimensional dynamical systems via
subdivision and continuation methods. These approximations give a topological
one-to-one image of the original set. In order to additionally reveal their
geometry we use diffusion mapst o find intrinsic coordinates. We illustrate our
results on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky
equation, as well as for the attractor of the Mackey-Glass delay differential
equation.
2019
eng
arXiv:1902.08824
Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.
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.
R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).
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.
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.
@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} }
Gerlach, R., Koltai, P., & Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. In <i>arXiv:1902.08824</i>.
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