The Lorenz system
The three movies below show how the stable manifold of the origin of the Lorenz system lies in the three-dimensional phase space. We refer to the text for more details concerning the system and the computations.
|Rotating the stable manifold as computed by [Worfolk 1997] about the z-axis (550K).|
|Rotating the stable manifold as computed by our algorithm about the z-axis (250K).|
|Zooming in shows how the stable manifold and the attractor are intertwined without intersecting. This animation also shows that the algorithm stopped because the Foliation Condition was no longer satisfied (480K).|
Quasiperiodically forced Hénon map
With this example we demonstrate how the algorithm generates the manifolds: they grow with constant speed in each leaf.
|Growing the stable and unstable manifolds of the invariant circles by adding rings in the computation (270K).|
|Zooming in on the attractor makes it clear that the algorithm is not affected by the dynamics on the manifolds (450K).|
Written by: Bernd Krauskopf
& Hinke Osinga
Created: May 27 1997 --- Last modified: Wed Jul 2 10:51:04 1997