S17 Class 24: Geometry of chaos

 

Before class, watch the lecture material linked below.
Post at least one question or comment on Piazza (access via Canvas or directly).  See "Check Yourself" Q1 for details.
Check yourself via the Class 24 Check Yourself on Canvas (Due by 11:59pm on Sun Apr 23rd)
In class, we'll work on related ideas: (activity will be posted)
After class, complete the homework (problems due Friday Apr 28th)

Videos:
The first introduces the idea of stretching and folding(watch to 41:00), which leads to fractal structure in an attractor and nonperiodic behavior in the system.  The second video is about the Hénon map, an illustrative example of this process (watch to 17:54).

Video details:
V01 (St)  |  Action of the vector field in a strange attractor  (7:  to 19:05)  |  12 min
V02 (St)  |  Geometry of chaos  (19:05 to 33:11)  |  14 min
V03 (St)  |  Logistic map has stretching and folding  (33:50 to 41:00)  |  7 min
V04 (St)  |  Henon map example (00:56 to 17:54)  |  17 min