文档介绍：Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
Springer, 2000.
Aspects on Data Analysis and Visualization for
Complex Dynamical Systems
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J. Becker , D. Burkle¨ , R.-T. Happe , T. Preußer , M. Rumpf , M. Spielberg , and
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R. Strzodka
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Universitat¨ Freiburg
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Universitat¨ Bonn
Abstract. Flow visualization is an indispensible tool for the understandig plex flow
phenomena putational fluid dynamics and the analysis of dynamical systems. In this
note we will present several ways for an effective post processing of fluid flows and flows
on invariant manifolds of dynamical systems. Feature extraction techniques will be present
which reduce the informational content of large timedependent data sets to its mainly inters-
esting essence. Futhermore, we present visualization approaches which are based on partial
differential equations. Similar to the modelling of physical phenomena by partial differential
equations, in the postprocessing of data such equations naturally arise as well. Finally, the
method for the dense covering of an invariant manifold with streamlines is outlined, which
enables us to represent the geometry of the objects, statistical information on it, and the local
flow properties at the same time.
1 Introduction
The understanding plex structures in dynamical systems is a challenging sub-
ject not only from the analytical or numerical point of view. Visualization serves as
a tool to get insight in solution structures and their dynamical behaviour. Frequently,
standard methods for a graphical representation break down almost at the beginning.
For instance the visualization of timedependent vector fields by arrow icons leads to
visual clutter, or drawing single orbits on invariant manifolds often hides important
features of this object. Furthermore, for timedependent problems especially in 3D,
a drawing plicated geometric pattern often hides essential information, e. g.
in terms of critical points,