Invariant Manifold Movies:
"Lorenz System" Example
The following movies illustrate the stable manifold of the origin
in the Lorenz system for the canonical parameter values.
In all of the following the color indicates the
distance-to-origin-along-trajectory (sigma).
The stable manifold rotating about the z-axis.:
View 1:
Computed up to Sigma=120.
View 2:
Computed up to Sigma=150.
``Growing'' the manifold:
Two different views (rotated) of the stable manifold of the origin.
The manifold is displayed semi-transparently, except for the ``outer rim''
(opaque) representing the most recently added simplexes.
The attractor is shown in black.
View 1
View 2
Relevant Links:
-
Our paper on
"A fast method for approximating invariant manifolds".
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Invariant manifold movies for the
"Two Pendula Coupled by a Torsional Spring" example.
This is a joint project with
John Guckenheimer.