Class 21: Discrete Systems

Before class, watch the lecture material linked below
Then post questions or comments (or respond to others) on Piazza (access via Canvas or from the direct link on the course page)
Check yourself via Check Yourself 21 (by 11:59pm on Wed Nov 11th)
In class, we'll work on examples of these ideas 

After class, complete the homework

V00 (youtube)  |  (optional)  Chaos in the double pendulum  (all)  |  3 min
V01 (St)  |  1D map: Logistic map  (00:04 to 18:20)  |  18 min
V02 (St)  |  Period doubling bifurcations  (18:20 to 28:54)  |  10 min
When there are two points in the diagram there is a stable period-2 orbit. 
When there are 4 there is a stable period-4 orbit, etc.
V03 (youtube)  |  Reynolds experiment  (1:21 to 2:08)  |  1 min
This is the transition to turbulent flow as water velocity increases that Steve describes in V02.
V04 (St)  |  Logistic map orbit diagram  (34:18 to 42:57)  |  9 min
V05 (St)  |  Finding the period doubling point  (53:04 to 1:04:50)  |  12 min
V06 (St)  |  Finding the period-2 values  (1:04:50 to end)  |  10 min
Video:
63 min total