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Special Topics:Dynamical Systems

4-d Map by Eduardo Tabacman

  
Two 2-dimensional surfaces in 4D, projected to 3D. (The color, from green to blue, represents the fourth coordinate). The surfaces are points in R^4 that converge (for stable manifold) to a fixed point (roughly in the middle of the surfaces) under iteration of a symplectic map, or diverge (for unstable one).

How to make it: Made by iteration of a (small) grid around the fixed point, in the directions of the eigenvectors of the Jacobian of the map. Viewed with geomview (4d-module).

Image created: 4/92

[4-d Map]

Copyright © 4/92 by The Geometry Center, Univerity of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 5k gif), medium (500x314 36k gif), or original size (895x561 434k tiff).

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Created: Sat May 22 23:17:47 CDT 1999 --- Last modified: Sat May 22 23:17:47 CDT 1999