Last thought for the day, from Does God Play Dice (Ian Stewart, 1989):
To a topologist, squares and circles are the same, since each can be continuously deformed into the other.
Bottom line...the Logistic equation in was nice because we could easily see the bifurcation points (and hear them).
In higher dimensional systems, it appears that the standard way of portraying bifurcations on paper or a computer screen is to look at Poincare sections.
More to follow...
Here is my repository of articles, videos, etc. using my ASU Google Drive.
https://drive.google.com/open?id=0B9oPg7GYw1qnbFIyZzdUY0Z1b00
Regards,
Brenda
FYI, I'm having trouble uploading a .pdf document with a technical article. Posthaven appears to be having difficulties rendering the equations in the article. I'll try another method and re-post.
I think it is a display issue on Posthaven. The file can still be downloaded accurately. I've also uploaded it to my ASU Google Drive and created a link to it inside the post.
-Brenda
Hmm...this might tell the story of bifurcations in multi-dimensional spaces, starting with the Lorenz equations in 1D.
https://drive.google.com/a/asu.edu/file/d/0B9oPg7GYw1qnYmNXa3M1Wng2Zk0/view?usp=sharing