Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems
Gerlach, Raphael
Koltai, Péter
Dellnitz, Michael
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
info:eu-repo/semantics/preprint
doc-type:preprint
text
https://ris.uni-paderborn.de/record/16711
Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems. <i>arXiv:190208824</i>. 2019.
eng
info:eu-repo/semantics/closedAccess