Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems

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 geometr...

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Veröffentlicht in:	arXiv.org 2019-02
Hauptverfasser:	Gerlach, Raphael, Koltai, Péter, Dellnitz, Michael
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Attractors (mathematics) Chaos theory Continuation methods Differential equations Dynamical systems Embedded systems Manifolds (mathematics)
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creator	Gerlach, Raphael Koltai, Péter Dellnitz, Michael
description	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.
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subjects	Approximation Attractors (mathematics) Chaos theory Continuation methods Differential equations Dynamical systems Embedded systems Manifolds (mathematics)
title	Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems
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