The Lorenz system is the three-dimensional vector field
We choose the standard parameter values
= 10,
= 28, but
take 
=
0.4. The two-dimensional stable manifold of the origin interacts now
with an attracting periodic orbit. The colored bands on the manifold
show the steps that are taken by the algorithm. Note how the algorithm
slows down each time a new helix around the z-axis is being formed.
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Still images of the manifold at several instances during the computation. As the manifold grows, it wraps around the attractor, eventually covering it completely. |
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The animated gif shows how the stable manifold grows, while it rotates about the z-axis (1.2MB). |