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S17 Class 22: Period doubling

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 22 Check Yourself on Canvas (Due by 11:59pm on Sun Apr 16th)
In class, we'll work on related ideas: (activity will be posted)
After class, complete the homework (problems due Friday Apr 28th)
 

V01 (Sarah)  |  Structure in the orbit diagram (All)  |  (3 min)
V02 (Sarah)  |  Period 3 and 5 in the logistic (All)  |  (4 min)
V03 (Sarah)  |  Other orbit diagrams for one-peaked maps (All)  |  (2 min)
V04 (St)  |  Period doubling route to chaos  (54:44-1:11:55)  |  (15 min)
V05 (St)  |  Super stable cycles (we're skipping the intro to the idea of superstability)  (10:15-14:30)  |  (4 min)
V06 (St)  |  Super stable orbits in the figtree diagram  (14:30-20:20)  |  (6 min)
skip 4 min of questions
V07 (St)  |  Self-similarity in figtree diagram  (24:18 to 36:18)  |  12 min
Note that he compared f(x,R1) and f^2(x,R2), so the value of r changed between the maps.
V08 (St)  |  Shifting and rescaling  (36:18 to 50:00)  |  14 min
V09 (St)  |  Source of universality (50:00 to 59:10)  |  9 min

We will learn more about g in class on Monday.

Videos:
71 min.